Journal articles: 'Moore-Penrose pseudoinverses'

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Stanimirovic, Predrag, Xue-Zhong Wang, and Haifeng Ma. "Complex ZNN for computing time-varying weighted pseudo-inverses." Applicable Analysis and Discrete Mathematics 13, no. 1 (2019): 131–64. http://dx.doi.org/10.2298/aadm170628019s.

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We classify, extend and unify various generalizations of weighted Moore-Penrose inverses in indefinite inner product spaces. New kinds of generalized inverses are introduced for this purpose. These generalized inverses are included in the more general class called as the weighted indefinite pseudoinverses (WIPI), which represents an extension of the Minkowski inverse (MI), the weighted Minkowski inverse (WMI), and the generalized weighted Moore- Penrose (GWM-P) inverse. The WIPI generalized inverses are introduced on the basis of two Hermitian invertible matrices and two Hermitian involuntary matrices and represented as particular outer inverses with prescribed ranges and null spaces, in terms of appropriate full-rank and limiting representations. Application of introduced generalized inverses in solving some indefinite least squares problems is considered. New Zeroing Neural Network (ZNN) models for computing the WIPI are developed using derived full-rank and limiting representations. The convergence behavior of the proposed ZNN models is investigated. Numerical simulation results are presented.

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Sun Zhou, and Kangkang Zhang. "Structure-Specific Neural Networks for Parallel Computation of All Types of Moore-Penrose Pseudoinverses." Journal of Convergence Information Technology 7, no. 20 (November 30, 2012): 8–16. http://dx.doi.org/10.4156/jcit.vol7.issue20.2.

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Klimczak, Marek, and Witold Cecot. "On Moore-Penrose Pseudoinverse Computation for Stiffness Matrices Resulting from Higher Order Approximation." Mathematical Problems in Engineering 2019 (February 24, 2019): 1–16. http://dx.doi.org/10.1155/2019/5060397.

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Computing the pseudoinverse of a matrix is an essential component of many computational methods. It arises in statistics, graphics, robotics, numerical modeling, and many more areas. Therefore, it is desirable to select reliable algorithms that can perform this operation efficiently and robustly. A demanding benchmark test for the pseudoinverse computation was introduced. The stiffness matrices for higher order approximation turned out to be such tough problems and therefore can serve as good benchmarks for algorithms of the pseudoinverse computation. It was found out that only one algorithm, out of five known from literature, enabled us to obtain acceptable results for the pseudoinverse of the proposed benchmark test.

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Caltenco, J. H., José Luis Lopez-Bonilla, B. E. Carvajal-Gámez, and P. Lam-Estrada. "Singular Value Decomposition." Bulletin of Society for Mathematical Services and Standards 11 (September 2014): 13–20. http://dx.doi.org/10.18052/www.scipress.com/bsmass.11.13.

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We study the SVD of an arbitrary matrix Anxm, especially its subspaces of activation, which leads in natural manner to pseudoinverse of Moore-Bjenhammar-Penrose. Besides, we analyze the compatibility of linear systems and the uniqueness of the corresponding solution, and our approach gives the Lanczos classification for these systems.

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Ataei, Alireza. "Improved Qrginv Algorithm for Computing Moore-Penrose Inverse Matrices." ISRN Applied Mathematics 2014 (March 12, 2014): 1–5. http://dx.doi.org/10.1155/2014/641706.

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Katsikis et al. presented a computational method in order to calculate the Moore-Penrose inverse of an arbitrary matrix (including singular and rectangular) (2011). In this paper, an improved version of this method is presented for computing the pseudo inverse of an m×n real matrix A with rank r>0. Numerical experiments show that the resulting pseudoinverse matrix is reasonably accurate and its computation time is significantly less than that obtained by Katsikis et al.

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Górecki, Tomasz, and Maciej Łuczak. "STACKED REGRESSION WITH A GENERALIZATION OF THE MOORE-PENROSE PSEUDOINVERSE." Statistics in Transition. New Series 18, no. 3 (2017): 443–58. http://dx.doi.org/10.21307/stattrans-2016-080.

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Shore, Aimee, and William M. Hartmann. "Improvements in transaural synthesis with the Moore-Penrose pseudoinverse matrix." Journal of the Acoustical Society of America 143, no. 3 (March 2018): 1938. http://dx.doi.org/10.1121/1.5036337.

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Barata, João Carlos Alves, and Mahir Saleh Hussein. "The Moore–Penrose Pseudoinverse: A Tutorial Review of the Theory." Brazilian Journal of Physics 42, no. 1-2 (December 16, 2011): 146–65. http://dx.doi.org/10.1007/s13538-011-0052-z.

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Stanimirović, Predrag S., Vasilios N. Katsikis, and Igor Stojanović. "Computing the Pseudoinverse of Specific Toeplitz Matrices Using Rank-One Updates." Mathematical Problems in Engineering 2016 (2016): 1–16. http://dx.doi.org/10.1155/2016/9065438.

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Application of the pure rank-one update algorithm as well as a combination of rank-one updates and the Sherman-Morrison formula in computing the Moore-Penrose inverse of the particular Toeplitz matrix is investigated in the present paper. Such Toeplitz matrices appear in the image restoration process and in many scientific areas that use the convolution. Four different approaches are developed, implemented, and tested on a number of numerical experiments.

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Miljkovic, Sladjana, Marko Miladinovic, Predrag Stanimirovic, and Igor Stojanovic. "Application of the pseudoinverse computation in reconstruction of blurred images." Filomat 26, no. 3 (2012): 453–65. http://dx.doi.org/10.2298/fil1203453m.

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We present a direct method for removing uniform linear motion blur from images. The method is based on a straightforward construction of the Moore-Penrose inverse of the blurring matrix for a given mathematical model. The computational load of the method is decreased significantly with respect to other competitive methods, while the resolution of the restored images remains at a very high level. The method is implemented in the programming package MATLand respective numerical examples are presented.

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Ferreira Mamede, Ana Camila, José Roberto Camacho, Rui Esteves Araújo, and Igor Santos Peretta. "Moore-Penrose pseudo-inverse and artificial neural network modeling in performance prediction of switched reluctance machine." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 39, no. 6 (November 23, 2020): 1411–30. http://dx.doi.org/10.1108/compel-11-2019-0449.

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Purpose The purpose of this paper is to present the Moore-Penrose pseudoinverse (PI) modeling and compare with artificial neural network (ANN) modeling for switched reluctance machine (SRM) performance. Design/methodology/approach In a design of an SRM, there are a number of parameters that are chosen empirically inside a certain interval, therefore, to find an optimal geometry it is necessary to define a good model for SRM. The proposed modeling uses the Moore-Penrose PI for the resolution of linear systems and finite element simulation data. To attest to the quality of PI modeling, a model using ANN is established and the two models are compared with the values determined by simulations of finite elements. Findings The proposed PI model showed better accuracy, generalization capacity and lower computational cost than the ANN model. Originality/value The proposed approach can be applied to any problem as long as experimental/computational results can be obtained and will deliver the best approximation model to the available data set.

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Górecki, Tomasz, and Maciej Łuczak. "Linear discriminant analysis with a generalization of the Moore–Penrose pseudoinverse." International Journal of Applied Mathematics and Computer Science 23, no. 2 (June 1, 2013): 463–71. http://dx.doi.org/10.2478/amcs-2013-0035.

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The Linear Discriminant Analysis (LDA) technique is an important and well-developed area of classification, and to date many linear (and also nonlinear) discrimination methods have been put forward. A complication in applying LDA to real data occurs when the number of features exceeds that of observations. In this case, the covariance estimates do not have full rank, and thus cannot be inverted. There are a number of ways to deal with this problem. In this paper, we propose improving LDA in this area, and we present a new approach which uses a generalization of the Moore-Penrose pseudoinverse to remove this weakness. Our new approach, in addition to managing the problem of inverting the covariance matrix, significantly improves the quality of classification, also on data sets where we can invert the covariance matrix. Experimental results on various data sets demonstrate that our improvements to LDA are efficient and our approach outperforms LDA.

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Boman, Eugene. "The Moore-Penrose Pseudoinverse of an Arbitrary, Square, k -circulant Matrix." Linear and Multilinear Algebra 50, no. 2 (January 2002): 175–79. http://dx.doi.org/10.1080/03081080290019559.

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Carp, Doina, Ioana Pomparău, and Constantin Popa. "Weaker assumptions for convergence of extended block Kaczmarz and Jacobi projection algorithms." Analele Universitatii "Ovidius" Constanta - Seria Matematica 25, no. 1 (January 26, 2017): 49–60. http://dx.doi.org/10.1515/auom-2017-0004.

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Abstract Recent developments in the field of image reconstruction have given rise to the use of projective iterative methods, such as Kaczmarz and Jacobi, when solving inconsistent linear least squares problems. In this paper we try to generalize previous results concerning extended block versions of these two algorithms. We replace the inverse operator with the Moore-Penrose pseudoinverse and try to prove convergence under weaker assumptions. In order to accomplish this task, we show that these algorithms are special cases of a general iterative process for which convergence is already established.

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McCartin, Brian J. "Pseudoinverse formulation of Rayleigh-Schrödinger perturbation theory for the symmetric matrix eigenvalue problem." Journal of Applied Mathematics 2003, no. 9 (2003): 459–85. http://dx.doi.org/10.1155/s1110757x03303092.

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A comprehensive treatment of Rayleigh-Schrödinger perturbation theory for the symmetric matrix eigenvalue problem is furnished with emphasis on the degenerate problem. The treatment is simply based upon the Moore-Penrose pseudoinverse thus distinguishing it from alternative approaches in the literature. In addition to providing a concise matrix-theoretic formulation of this procedure, it also provides for the explicit determination of that stage of the algorithm where each higher-order eigenvector correction becomes fully determined. The theory is built up gradually with each successive stage appended with an illustrative example.

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Hosseinpour, A. "Extension of Moore-Penrose Pseudoinverse to Solve Nonsquare Fuzzy System of Linear Equations." Asian Research Journal of Mathematics 8, no. 2 (January 15, 2018): 1–11. http://dx.doi.org/10.9734/arjom/2018/38351.

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Balatkhanova, Elita, Irina Erofeeva, and Victor Afonin. "Regression assessment of the model based on the experimental planning matrix in composite materials’ analysis problems." E3S Web of Conferences 281 (2021): 03015. http://dx.doi.org/10.1051/e3sconf/202128103015.

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An automated coefficients calculation of the regression model based on the experimental data in the form of a planning matrix is considered. The calculations are based on polynomial regression with possible consideration of the interaction effects between its factors. The application of the Moore – Penrose pseudoinverse matrix for determining the regression equation coefficients is shown. The choice of the calculated planning matrix is carried out taking into account the determination coefficient value and the factors’ calculated matrix rank. Calculation verification is carried out using the rank correlation between the experimental and calculated response functions. The experimental part of the work is given to determine the dependence of fungal resistance and fungicidal properties of filled cement composites on the type and grain size composition of the filler.

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Xing, Jianwei, and Gangtie Zheng. "Stress Field Gradient Analysis Technique Using Lower-OrderC0Elements." Mathematical Problems in Engineering 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/457046.

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For evaluating the stress gradient, a mathematical technique based on the stress field of lower-orderC0elements is developed in this paper. With nodal stress results and location information, an overdetermined and inconsistent equation of stress gradient is established and the minimum norm least squares solution is obtained by the Moore-Penrose pseudoinverse. This technique can be applied to any element type in comparison with the superconvergent patch (SCP) recovery for the stress gradient, which requires the quadratic elements at least and has to invert the Jacobi and Hessian matrices. The accuracy and validity of the presented method are demonstrated by two examples, especially its merit of achieving high accuracy with lower-order linearC0elements. This method can be conveniently introduced into the general finite element analysis programs as a postprocessing module.

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Veerasamy, Veerapandiyan, Noor Izzri Abdul Wahab, Rajeswari Ramachandran, Salah Kamel, Mohammad Lutfi Othman, Hashim Hizam, and Rizwan Farade. "Power flow solution using a novel generalized linear Hopfield network based on Moore–Penrose pseudoinverse." Neural Computing and Applications 33, no. 18 (March 12, 2021): 11673–89. http://dx.doi.org/10.1007/s00521-021-05843-9.

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Shehda, L. M. "DEGENERATE BOUNDARY-VALUE PROBLEMS WITH A PERTURBING MATRIX FOR A DERIVATIVE." PRECARPATHIAN BULLETIN OF THE SHEVCHENKO SCIENTIFIC SOCIETY Number, no. 1(59) (January 28, 2021): 29–37. http://dx.doi.org/10.31471/2304-7399-2020-1(59)-29-37.

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In the paper, there is considered degenerated Noether boundary value problem with a perturbing matrix for a derivative, in which the boundary condition is given by a linear vector functional. We have proposed an algorithm to consrtuct a set of linearly independent solutions of boundary value problems with a small parameter in the general case, when the number of boundary conditions given by a linear vector functional does not match with the number of unknowns in a degenerate differential system. There is used the technique of pseudoinverse Moore-Penrose matrices. Applying the Vishik-Lyusternik method, the solution of the boundary value problem is obtained as part of the Laurent series in powers of small parameter. We obtain conditions for the bifurcation of solutions of linear degenerated Noether boundary-value problems with a small parameter under the assumption that the unperturbed degenerated differential system can be reduced to central canonical form.

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Arts, M. J., D. S. Prinsloo, M. J. Bentum, and A. B. Smolders. "Frequency Interpolation of LOFAR Embedded Element Patterns Using Spherical Wave Expansion." International Journal of Antennas and Propagation 2021 (June 15, 2021): 1–13. http://dx.doi.org/10.1155/2021/5598380.

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This paper describes the use of spherical wave expansion (SWE) to model the embedded element patterns of the LOFAR low-band array. The goal is to reduce the amount of data needed to store the embedded element patterns. The coefficients are calculated using the Moore–Penrose pseudoinverse. The Fast Fourier Transform (FFT) is used to interpolate the coefficients in the frequency domain. It turned out that the embedded element patterns can be described by only 41.8% of the data needed to describe them directly if sampled at the Nyquist rate. The presented results show that a frequency resolution of 1 MHz is needed for proper interpolation of the spherical wave coefficients over the 80 MHz operating frequency band of the LOFAR low-band array. It is also shown that the error due to interpolation using the FFT is less than the error due to linear interpolation or cubic spline interpolation.

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Tokarzewski, J. "System zeros analysis via the Moore-Penrose pseudoinverse and SVD of the first nonzero Markov parameter." IEEE Transactions on Automatic Control 43, no. 9 (1998): 1285–91. http://dx.doi.org/10.1109/9.718619.

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Arias, Fernando X., Heidy Sierra, and Emmanuel Arzuaga. "Improving execution time for supervised sparse representation classification of hyperspectral images using the Moore–Penrose pseudoinverse." Journal of Applied Remote Sensing 13, no. 02 (June 13, 2019): 1. http://dx.doi.org/10.1117/1.jrs.13.026512.

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Boichuk, A., J. Diblík, D. Khusainov, and M. Růžičková. "Boundary-Value Problems for Weakly Nonlinear Delay Differential Systems." Abstract and Applied Analysis 2011 (2011): 1–19. http://dx.doi.org/10.1155/2011/631412.

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Conditions are derived of the existence of solutions of nonlinear boundary-value problems for systems ofnordinary differential equations with constant coefficients and single delay (in the linear part) and with a finite number of measurable delays of argument in nonlinearity:ż(t)=Az(t-τ)+g(t)+εZ(z(hi(t),t,ε), t∈[a,b], assuming that these solutions satisfy the initial and boundary conditionsz(s):=ψ(s) if s∉[a,b], lz(⋅)=α∈Rm. The use of a delayed matrix exponential and a method of pseudoinverse by Moore-Penrose matrices led to anexplicitandanalyticalform of sufficient conditions for the existence of solutions in a given space and, moreover, to the construction of an iterative process for finding the solutions of such problems in a general case when the number of boundary conditions (defined by a linear vector functionall) does not coincide with the number of unknowns in the differential system with a single delay.

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NOII, Nima, Iman AGHAYAN, Iman HAJIRASOULIHA, and Mehmet Metin KUNT. "A new hybrid method for size and topology optimization of truss structures using modified ALGA and QPGA." JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 23, no. 2 (February 12, 2016): 252–62. http://dx.doi.org/10.3846/13923730.2015.1075420.

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Modified Augmented Lagrangian Genetic Algorithm (ALGA) and Quadratic Penalty Function Genetic Algorithm (QPGA) optimization methods are proposed to obtain truss structures with minimum structural weight using both continuous and discrete design variables. To achieve robust solutions, Compressed Sparse Row (CSR) with reordering of Cholesky factorization and Moore Penrose Pseudoinverse are used in case of non-singular and singular stiffness matrix, respectively. The efficiency of the proposed nonlinear optimization methods is demonstrated on several practical examples. The results obtained from the Pratt truss bridge show that the optimum design solution using discrete parameters is 21% lighter than the traditional design with uniform cross sections. Similarly, the results obtained from the 57-bar planar tower truss indicate that the proposed design method using continuous and discrete design parameters can be up to 29% and 9% lighter than traditional design solutions, respectively. Through sensitivity analysis, it is shown that the proposed methodology is robust and leads to significant improvements in convergence rates, which should prove useful in large-scale applications.

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Chuiko, Sergei, Elena Chuiko, and Yaroslav Kalinichenko. "On a regularization method for solving linear Noetherian boundary value problem for difference system." Proceedings of the Institute of Applied Mathematics and Mechanics NAS of Ukraine 32 (December 28, 2018): 133–48. http://dx.doi.org/10.37069/1683-4720-2018-32-14.

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The article proposes unusual regularization conditions as well as a scheme for finding bounded solutions of the linear Noetherian boundary value problem for a system of difference equations in the critical case, significantly using the Moore-Penrose matrix pseudo-inversion technology. The problem posed in the article continues the study of the a sufficient condition for solvability and regularization conditions for linear Noetherian boundary value problems in the critical case given in the monographs by A.N. Tikhonov, V.Ya. Arsenin, S.G. Krein, A.M. Samoilenko, N.V. Azbelev, V.P. Maksimov, L.F. Rakhmatullina and A.A. Boichuk. The general case is studied in which a linear bounded operator corresponding to a homogeneous part of a linear Noetherian boundary value problem has no inverse. The noninvertibility of the operators corresponding to a homogeneous part of a linear Noetherian boundary value problem is a consequence of the fact that the number of boundary conditions does not coincide with the number of unknown variables of the difference equations. Using the theory of generalized inverse operators and Moore-Penrose pseudoinverse matrix in the article, a generalized Green operator is constructed and the type of a linear perturbation of a regularized linear Noether boundary value problem for a system of difference equations in the critical case is found. The proposed regularization conditions, as well as the scheme for finding of bounded solutions to linear Noetherian boundary value problems for a system of difference equations in the critical case, are illustrated in details with examples. In contrast to the earlier articles of the authors, the regularization problem for a linear Noether boundary value problem for a system of difference equations in the critical case has been resolved constructively, and sufficient conditions has been obtained for the existence of a bounded solution to the regularization problem.

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Jhurani, Chetan, and Leszek Demkowicz. "Multiscale modeling using goal-oriented adaptivity and numerical homogenization. Part II: Algorithms for the Moore–Penrose pseudoinverse." Computer Methods in Applied Mechanics and Engineering 213-216 (March 2012): 418–26. http://dx.doi.org/10.1016/j.cma.2011.06.003.

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Carp, Doina, Constantin Popa, and Cristina Serban. "A general iterative solver for unbalanced inconsistent transportation problems." Archives of Transport 37, no. 1 (March 31, 2016): 7–13. http://dx.doi.org/10.5604/08669546.1203199.

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The transportation problem, as a particular case of a linear programme, has probably the highest relative frequency with which appears in applications. At least in its classical formulation, it involves demands and supplies. When, for practical reasons, the total demand cannot satisfy the total supply, the problem becomes unbalanced and inconsistent, and must be reformulated as e.g. finding a least squares solution of an inconsistent system of linear inequalities. A general iterative solver for this class of problems has been proposed by S. P. Han in his 1980 original paper. The drawback of Han’s algorithm consists in the fact that it uses in each iteration the computation of the Moore-Penrose pseudoinverse numerical solution of a subsystem of the initial one, which for bigger dimensions can cause serious computational troubles. In order to overcome these difficulties we propose in this paper a general projection-based minimal norm solution approximant to be used within Han-type algorithms for approximating least squares solutions of inconsistent systems of linear inequalities. Numerical experiments and comparisons on some inconsistent transport model problems are presented.

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Pletl, Szilveszter, and Bela Lantos. "Advanced Robot Control Algorithms Based on Fuzzy, Neural and Genetic Methods." Journal of Advanced Computational Intelligence and Intelligent Informatics 5, no. 2 (March 20, 2001): 81–89. http://dx.doi.org/10.20965/jaciii.2001.p0081.

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Soft computing (fuzzy systems, neural networks and genetic algorithms) can solve difficult problems, especially non-linear control problems such as robot control. In the paper two algorithms have been presented for the nonlinear control of robots. The first algorithm applies a new neural network based controller structure and a learning method with stability guarantee. The controller consists of the nonlinear prefilter, the feedforward neural network and feadback PD controllers. The fast learning algorithm of the neural network is based on Moore-Penrose pseudoinverse technique. The second algorithm is based on a decentralized hierarchical neuro-fuzzy controller structure. New approach to evolutionary algorithms called LEGA optimizes the controller during the teaching period. LEGA combines the standard GA technique with numerical optimum seeking for a limited number of elite individuels in each generation. It can lead to global optimum in few generations. The soft computing based nonlinear control algorithms have been applied for the control of a rigid link flexible joint (RLFJ) 4 DOF SCARA robot in order to prove the effectiveness of the proposed methods.

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Päschke, E., R. Leinweber, and V. Lehmann. "A one year comparison of 482 MHz radar wind profiler, RS92-SGP Radiosonde and 1.5 μm Doppler Lidar wind measurements." Atmospheric Measurement Techniques Discussions 7, no. 11 (November 19, 2014): 11439–79. http://dx.doi.org/10.5194/amtd-7-11439-2014.

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Abstract. We present the results of a one-year quasi-operational testing of the 1.5 μm StreamLine Doppler lidar developed by Halo Photonics from 2 October 2012 to 2 October 2013. The system was configured to continuously perform a velocity-azimuth display (VAD) scan pattern using 24 azimuthal directions with a constant beam elevation angle of 75°. Radial wind estimates were selected using a rather conservative signal-to-noise ratio (SNR) based threshold of −18.2 dB (0.015). A 30 min average wind vector was calculated based on the assumption of a horizontally homogeneous wind field through a singular-value decomposed Moore–Penrose pseudoinverse of the overdetermined linear system. A strategy for a quality control of the retrieved wind vector components is outlined which is used to ensure consistency between the retrieved winds and the assumptions inherent to the employed wind vector retrieval. Finally, the lidar measurements are compared with operational data from a collocated 482 MHz radar wind profiler running in a four-beam Doppler beam swinging (DBS) mode and winds from operational radiosonde measurements. The intercomparisons show that the Doppler lidar is a reliable system for operational wind measurements in the atmospheric boundary layer (ABL).

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THEODORIDIS, DIMITRIOS, YIANNIS BOUTALIS, and MANOLIS CHRISTODOULOU. "INDIRECT ADAPTIVE CONTROL OF UNKNOWN MULTI VARIABLE NONLINEAR SYSTEMS WITH PARAMETRIC AND DYNAMIC UNCERTAINTIES USING A NEW NEURO-FUZZY SYSTEM DESCRIPTION." International Journal of Neural Systems 20, no. 02 (April 2010): 129–48. http://dx.doi.org/10.1142/s0129065710002310.

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The indirect adaptive regulation of unknown nonlinear dynamical systems with multiple inputs and states (MIMS) under the presence of dynamic and parameter uncertainties, is considered in this paper. The method is based on a new neuro-fuzzy dynamical systems description, which uses the fuzzy partitioning of an underlying fuzzy systems outputs and high order neural networks (HONN's) associated with the centers of these partitions. Every high order neural network approximates a group of fuzzy rules associated with each center. The indirect regulation is achieved by first identifying the system around the current operation point, and then using its parameters to device the control law. Weight updating laws for the involved HONN's are provided, which guarantee that, under the presence of both parameter and dynamic uncertainties, both the identification error and the system states reach zero, while keeping all signals in the closed loop bounded. The control signal is constructed to be valid for both square and non square systems by using a pseudoinverse, in Moore-Penrose sense. The existence of the control signal is always assured by employing a novel method of parameter hopping instead of the conventional projection method. The applicability is tested on well known benchmarks.

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Päschke, E., R. Leinweber, and V. Lehmann. "An assessment of the performance of a 1.5 μm Doppler lidar for operational vertical wind profiling based on a 1-year trial." Atmospheric Measurement Techniques 8, no. 6 (June 3, 2015): 2251–66. http://dx.doi.org/10.5194/amt-8-2251-2015.

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Abstract. We present the results of a 1-year quasi-operational testing of the 1.5 μm StreamLine Doppler lidar developed by Halo Photonics from 2 October 2012 to 2 October 2013. The system was configured to continuously perform a velocity-azimuth display scan pattern using 24 azimuthal directions with a constant beam elevation angle of 75°. Radial wind estimates were selected using a rather conservative signal-to-noise ratio based threshold of −18.2 dB (0.015). A 30 min average profile of the wind vector was calculated based on the assumption of a horizontally homogeneous wind field through a Moore–Penrose pseudoinverse of the overdetermined linear system. A strategy for the quality control of the retrieved wind vector components is outlined for ensuring consistency between the Doppler lidar wind products and the inherent assumptions employed in the wind vector retrieval. Quality-controlled lidar measurements were compared with independent reference data from a collocated operational 482 MHz radar wind profiler running in a four-beam Doppler beam swinging mode and winds from operational radiosonde measurements. The intercomparison results reveal a particularly good agreement between the Doppler lidar and the radar wind profiler, with root mean square errors ranging between 0.5 and 0.7 m s−1 for wind speed and between 5 and 10° for wind direction. The median of the half-hourly averaged wind speed for the intercomparison data set is 8.2 m s−1, with a lower quartile of 5.4 m s−1 and an upper quartile of 11.6 m s−1.

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Chuiko, Sergei, and Olga Nesmelova. "About the equilibrium positions of a matrix differential-algebraic boundary value problem." Proceedings of the Institute of Applied Mathematics and Mechanics NAS of Ukraine 33 (December 27, 2019): 218–31. http://dx.doi.org/10.37069/1683-4720-2019-33-17.

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In the article we found the solvability conditions and the construction of the generalized Green operator of the linear Noetherian matrix differential-algebraic boundary value problem. We obtained sufficient conditions of transformationsof the matrix differential-algebraic equation to a traditional differential-algebraic equation with an unknown in the form of a column vector. The problem that reviewed in the article continues the study of solvability conditions for the linear Noetherian boundary value problems given in the monographs of M.V. Azbelev, V.P. Maksimov, L.F. Rakhmatullina, A.M. Samoilenko and A.A. Boichuk. We investigated the general case when the linear bounded operator corresponding to the homogeneous part of the linear Cauchy problem for the matrix differential-algebraic system does not have the reverse operator. We introduced the definition of the equilibrium positions of the matrix differential-algebraic system and the matrix differential-algebraic boundary-value problem to solve the matrix differential-algebraic boundary-value problem. We proposed sufficient conditions of existence and constructive schemes for finding the equilibrium positions of the matrix differential-algebraic system and the matrix differential-algebraic boundary value problem. The cases~of equilibrium positions of the matrix differential-algebraic system, which are constant matrices, and equilibrium positions depending on an independent variable are considered separately. To solve the matrix differential-algebraic boundary-value problem, we used the original solvability conditions and~the construction of the general solution of the Sylvester-type matrix equation, while the Moore-Penrose matrix pseudoinverse technique was essentially used. In the article we constructed the generalized Green operator of the linear Noetherian matrix differential-algebraic boundary value problem. The proposed solvability conditions and the construction of the generalized Green operator of the linear Noetherian matrix differential-algebraic boundary value problem, were illustrated in detail with examples.

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Hare, Warren, Gabriel Jarry–Bolduc, and Chayne Planiden. "Error bounds for overdetermined and underdetermined generalized centred simplex gradients." IMA Journal of Numerical Analysis, December 11, 2020. http://dx.doi.org/10.1093/imanum/draa089.

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Abstract Using the Moore–Penrose pseudoinverse this work generalizes the gradient approximation technique called the centred simplex gradient to allow sample sets containing any number of points. This approximation technique is called the generalized centred simplex gradient. We develop error bounds and, under a full-rank condition, show that the error bounds have ${\mathcal O}(\varDelta ^2)$, where $\varDelta $ is the radius of the sample set of points used. We establish calculus rules for generalized centred simplex gradients, introduce a calculus-based generalized centred simplex gradient and confirm that error bounds for this new approach are also ${\mathcal O}(\varDelta ^2)$. We provide several examples to illustrate the results and some benefits of these new methods.

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Wang, Na, Alan D. Wright, and Mark J. Balas. "Disturbance Accommodating Control Design for Wind Turbines Using Solvability Conditions." Journal of Dynamic Systems, Measurement, and Control 139, no. 4 (February 7, 2017). http://dx.doi.org/10.1115/1.4035097.

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In this paper, solvability conditions for disturbance accommodating control (DAC) have been discussed and applied on wind turbine controller design in above-rated wind speed to regulate rotor speed and to mitigate turbine structural loads. An asymptotically stabilizing DAC controller with disturbance impact on the wind turbine being totally canceled out can be found if certain conditions are fulfilled. Designing a rotor speed regulation controller without steady-state error is important for applying linear control methodology such as DAC on wind turbines. Therefore, solvability conditions of DAC without steady-state error are attractive and can be taken as examples when designing a multitask turbine controller. DAC controllers solved via Moore–Penrose Pseudoinverse and the Kronecker product are discussed, and solvability conditions of using them are given. Additionally, a new solvability condition based on inverting the feed-through D term is proposed for the sake of reducing computational burden in the Kronecker product. Applications of designing collective pitch and independent pitch controllers based on DAC are presented. Recommendations of designing a DAC-based wind turbine controller are given. A DAC controller motivated by the proposed solvability condition that utilizes the inverse of feed-through D term is developed to mitigate the blade flapwise once-per-revolution bending moment together with a standard proportional integral controller in the control loop to assist rotor speed regulation. Simulation studies verify the discussed solvability conditions of DAC and show the effectiveness of the proposed DAC control design methodology.

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Correia, Daniel, and Daniel N. Wilke. "How We Solve the Weights in Our Surrogate Models Matters." Journal of Mechanical Design 141, no. 7 (March 13, 2019). http://dx.doi.org/10.1115/1.4042622.

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The construction of surrogate models, such as radial basis function (RBF) and Kriging-based surrogates, requires an invertible (square and full rank matrix) or pseudoinvertible (overdetermined) linear system to be solved. This study demonstrates that the method used to solve this linear system may result in up to five orders of magnitude difference in the accuracy of the constructed surrogate model using exactly the same information. Hence, this paper makes the canonic and important point toward reproducible science: the details of solving the linear system when constructing a surrogate model must be communicated. This point is clearly illustrated on a single function, namely the Styblinski–Tang test function by constructing over 200 RBF surrogate models from 128 Latin Hypercubed sampled points. The linear system in the construction of each surrogate model was solved using LU, QR, Cholesky, Singular-Value Decomposition, and the Moore–Penrose pseudoinverse. As we show, the decomposition method influences the utility of the surrogate model, which depends on the application, i.e., whether an accurate approximation of a surrogate is required or whether the ability to optimize the surrogate and capture the optimal design is pertinent. Evidently the selection of the optimal hyperparameters based on the cross validation error also significantly impacts the utility of the constructed surrogate. For our problem, it turns out that selecting the hyperparameters at the lowest cross validation error favors function approximation but adversely affects the ability to optimize the surrogate model. This is demonstrated by optimizing each constructed surrogate model from 16 fixed initial starting points and recording the optimal designs. For our problem, selecting the optimal hyperparameter that coincides with the lowest monotonically decreasing function value significantly improves the ability to optimize the surrogate for most solution strategies.

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Journal articles on the topic 'Moore-Penrose pseudoinverses'

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