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Academic literature on the topic 'Gaussian Cubature Formulas'

Author: Grafiati
Published: 6 September 2023

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Journal articles on the topic "Gaussian Cubature Formulas"

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Lasserre, Jean B. "The existence of Gaussian cubature formulas." Journal of Approximation Theory 164, no. 5 (May 2012): 572–85. http://dx.doi.org/10.1016/j.jat.2012.01.004.

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Reztsov, A. V. "Nonnegative trigonometric polynomials in many variables and cubature formulas of Gaussian type." Mathematical Notes of the Academy of Sciences of the USSR 50, no. 5 (November 1991): 1142–46. http://dx.doi.org/10.1007/bf01157701.

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Bannai, Eiichi, Etsuko Bannai, Masatake Hirao, and Masanori Sawa. "On the existence of minimum cubature formulas for Gaussian measure on ℝ2 of degree t supported by $[\frac{t}{4}]+1$ circles." Journal of Algebraic Combinatorics 35, no. 1 (June 1, 2011): 109–19. http://dx.doi.org/10.1007/s10801-011-0295-3.

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Berens, H., H. J. Schmid, and Y. Xu. "Multivariate Gaussian cubature formulae." Archiv der Mathematik 64, no. 1 (January 1995): 26–32. http://dx.doi.org/10.1007/bf01193547.

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Schmid, H. J., and Yuan Xu. "On bivariate Gaussian cubature formulae." Proceedings of the American Mathematical Society 122, no. 3 (March 1, 1994): 833. http://dx.doi.org/10.1090/s0002-9939-1994-1209428-0.

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Jandrlic, Davorka, Miodrag Spalevic, and Jelena Tomanovic. "Error estimates for certain cubature formulae." Filomat 32, no. 20 (2018): 6893–902. http://dx.doi.org/10.2298/fil1820893j.

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We estimate the errors of selected cubature formulae constructed by the product of Gauss quadrature rules. The cases of multiple and (hyper-)surface integrals over n-dimensional cube, simplex, sphere and ball are considered. The error estimates are obtained as the absolute value of the difference between cubature formula constructed by the product of Gauss quadrature rules and cubature formula constructed by the product of corresponding Gauss-Kronrod or corresponding generalized averaged Gaussian quadrature rules. Generalized averaged Gaussian quadrature rule ?2l+1 is (2l + 1)-point quadrature formula. It has 2l + 1 nodes and the nodes of the corresponding Gauss rule Gl with l nodes form a subset, similar to the situation for the (2l + 1)-point Gauss-Kronrod rule H2l+1 associated with Gl. The advantages of bG2l+1 are that it exists also when H2l+1 does not, and that the numerical construction of ?2l+1, based on recently proposed effective numerical procedure, is simpler than the construction of H2l+1.
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Wang, Tianjing, Lanyong Zhang, and Sheng Liu. "Improved Robust High-Degree Cubature Kalman Filter Based on Novel Cubature Formula and Maximum Correntropy Criterion with Application to Surface Target Tracking." Journal of Marine Science and Engineering 10, no. 8 (August 4, 2022): 1070. http://dx.doi.org/10.3390/jmse10081070.

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Robust nonlinear filtering is an important method for tracking maneuvering targets in non-Gaussian noise environments. Although there are many robust filters for nonlinear systems, few of them have ideal performance for mixed Gaussian noise and non-Gaussian noise (such as scattering noise) in practical applications. Therefore, a novel cubature formula and maximum correntropy criterion (MCC)-based robust cubature Kalman filter is proposed. First, the fully symmetric cubature criterion and high-order divided difference are used to construct a new fifth-degree cubature formula using fewer symmetric cubature points. Then, a new cost function is obtained by combining the weighted least-squares method and the MCC loss criterion to deal with the abnormal values of non-Gaussian noise, which enhances the robustness; and statistical linearization methods are used to calculate the approximate result of the measurement process. Thus, the final fifth-degree divided difference–maximum correntropy cubature Kalman filter (DD-MCCKF) framework is constructed. A typical surface-maneuvering target-tracking simulation example is used to verify the tracking accuracy and robustness of the proposed filter. Experimental results indicate that the proposed filter has a higher tracking accuracy and better numerical stability than other common nonlinear filters in non-Gaussian noise environments with fewer cubature points used.
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Bojanov, Borislav D., and Dimitar K. Dimitrov. "Gaussian extended cubature formulae for polyharmonic functions." Mathematics of Computation 70, no. 234 (February 23, 2000): 671–84. http://dx.doi.org/10.1090/s0025-5718-00-01206-0.

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Orive, Ramón, Juan C. Santos-León, and Miodrag M. Spalević. "Cubature formulae for the Gaussian weight. Some old and new rules." ETNA - Electronic Transactions on Numerical Analysis 53 (2020): 426–38. http://dx.doi.org/10.1553/etna_vol53s426.

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Xu, Yuan. "On Zeros of Multivariate Quasi-Orthogonal Polynomials and Gaussian Cubature Formulae." SIAM Journal on Mathematical Analysis 25, no. 3 (May 1994): 991–1001. http://dx.doi.org/10.1137/s0036141092237200.

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Dissertations / Theses on the topic "Gaussian Cubature Formulas"

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Niime, Fabio Nosse [UNESP]. "Polinômios ortogonais em várias variáveis." Universidade Estadual Paulista (UNESP), 2011. http://hdl.handle.net/11449/86506.

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Made available in DSpace on 2014-06-11T19:22:18Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-02-24Bitstream added on 2014-06-13T20:28:32Z : No. of bitstreams: 1 niime_fn_me_sjrp.pdf: 457352 bytes, checksum: 318f01064234c003baca33cae4183d6d (MD5)
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
O objetivo des trabalho é estudar os polinômios ortogonais em várias variáveis com relação a um funcional linear, L e suas propriedades análogas às dos polinômios ortogonais em uma variável, tais como: a relação de três termos, a relação de recorrência de três termos, o teorema de Favard, os zeros comuns ea cubatura gaussiana. Além disso, apresentamos um método para gerar polinômios ortonormais em duas variáveis e alguns exemplos.
The aim here is to study the orthogonal polynomials in several variables with respect to a linear functional, L. also, to study its properties analogous to orthogonal polynomials in one variable, such as the theree term relation, the three term recurrence relation, Favard's theorem, the common zeros and Gaussian cubature. A method to generating orthonormal polynomials in two variables and some examples are presented.
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Book chapters on the topic "Gaussian Cubature Formulas"

1

Cuyt, Annie, Brahim Benouahmane, and Brigitte Verdonk. "Spherical Orthogonal Polynomials and Symbolic-Numeric Gaussian Cubature Formulas." In Computational Science - ICCS 2004, 557–60. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-24687-9_71.

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