Articles de revues : « Arbitrary precision »

1

D'Ariano, Giacomo M., et Matteo G. A. Paris. « Arbitrary precision in multipath interferometry ». Physical Review A 55, n^o 3 (1 mars 1997) : 2267–71. http://dx.doi.org/10.1103/physreva.55.2267.

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RODRIGUES, B. O., L. A. C. P. DA MOTA et L. G. S. DUARTE. « NUMERICAL CALCULATION WITH ARBITRARY PRECISION ». International Journal of Modern Physics E 16, n^o 09 (octobre 2007) : 3045–48. http://dx.doi.org/10.1142/s0218301307009014.

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The vast use of computers on scientific numerical computation makes the awareness of the limited precision that these machines are able to provide us an essential matter. A limited and insufficient precision allied to the truncation and rounding errors may induce the user to incorrect interpretation of his or her answer. In this work, we have developed a computational package to minimize this kind of error by offering arbitrary precision numbers and calculation. This is very important in Physics where we can work with numbers too small and too big simultaneously.

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Brisebarre, Nicolas, et Jean-Michel Muller. « Correctly Rounded Multiplication by Arbitrary Precision Constants ». IEEE Transactions on Computers 57, n^o 2 (février 2008) : 165–74. http://dx.doi.org/10.1109/tc.2007.70813.

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Ghazi, Kaveh R., Vincent Lefevre, Philippe Theveny et Paul Zimmermann. « Why and How to Use Arbitrary Precision ». Computing in Science & ; Engineering 12, n^o 3 (mai 2010) : 5. http://dx.doi.org/10.1109/mcse.2010.73.

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Lefevre, Vincent. « Correctly Rounded Arbitrary-Precision Floating-Point Summation ». IEEE Transactions on Computers 66, n^o 12 (1 décembre 2017) : 2111–24. http://dx.doi.org/10.1109/tc.2017.2690632.

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Graça, D. S., C. Rojas et N. Zhong. « Computing geometric Lorenz attractors with arbitrary precision ». Transactions of the American Mathematical Society 370, n^o 4 (31 octobre 2017) : 2955–70. http://dx.doi.org/10.1090/tran/7228.

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Ménissier-Morain, Valérie. « Arbitrary precision real arithmetic : design and algorithms ». Journal of Logic and Algebraic Programming 64, n^o 1 (juillet 2005) : 13–39. http://dx.doi.org/10.1016/j.jlap.2004.07.003.

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El-Araby, Esam, Ivan Gonzalez, Sergio Lopez-Buedo et Tarek El-Ghazawi. « A Convolve-And-MErge Approach for Exact Computations on High-Performance Reconfigurable Computers ». International Journal of Reconfigurable Computing 2012 (2012) : 1–14. http://dx.doi.org/10.1155/2012/925864.

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This work presents an approach for accelerating arbitrary-precision arithmetic on high-performance reconfigurable computers (HPRCs). Although faster and smaller, fixed-precision arithmetic has inherent rounding and overflow problems that can cause errors in scientific or engineering applications. This recurring phenomenon is usually referred to as numerical nonrobustness. Therefore, there is an increasing interest in the paradigm of exact computation, based on arbitrary-precision arithmetic. There are a number of libraries and/or languages supporting this paradigm, for example, the GNU multiprecision (GMP) library. However, the performance of computations is significantly reduced in comparison to that of fixed-precision arithmetic. In order to reduce this performance gap, this paper investigates the acceleration of arbitrary-precision arithmetic on HPRCs. A Convolve-And-MErge approach is proposed, that implements virtual convolution schedules derived from the formal representation of the arbitrary-precision multiplication problem. Additionally, dynamic (nonlinear) pipeline techniques are also exploited in order to achieve speedups ranging from 5x (addition) to 9x (multiplication), while keeping resource usage of the reconfigurable device low, ranging from 11% to 19%.

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Lee, JunKyu, Gregory D. Peterson, Dimitrios S. Nikolopoulos et Hans Vandierendonck. « AIR : Iterative refinement acceleration using arbitrary dynamic precision ». Parallel Computing 97 (septembre 2020) : 102663. http://dx.doi.org/10.1016/j.parco.2020.102663.

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Johansson, Fredrik. « Arb : Efficient Arbitrary-Precision Midpoint-Radius Interval Arithmetic ». IEEE Transactions on Computers 66, n^o 8 (1 août 2017) : 1281–92. http://dx.doi.org/10.1109/tc.2017.2690633.

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Alway, William G., et Jonathan A. Jones. « Arbitrary precision composite pulses for NMR quantum computing ». Journal of Magnetic Resonance 189, n^o 1 (novembre 2007) : 114–20. http://dx.doi.org/10.1016/j.jmr.2007.09.001.

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Boyer, W., et A. E. Lynas-Gray. « Evaluation of the Voigt function to arbitrary precision ». Monthly Notices of the Royal Astronomical Society 444, n^o 3 (septembre 2014) : 2555–60. http://dx.doi.org/10.1093/mnras/stu1606.

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Krämer, Walter. « Multiple/arbitrary precision interval computations in C-XSC ». Computing 94, n^o 2-4 (26 novembre 2011) : 229–41. http://dx.doi.org/10.1007/s00607-011-0174-8.

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Chi, Nguyen Van, Nguyen Hien Trung et Nguyen Doan Phuoc. « ABOUT THE ROBUSTNESS OF ADAPTIVE FEEDBACK LINEARIZATION CONTROLLER FOR INPUT PERTURBED UNCERTAIN FULLY-ACTUATED SYSTEMS ». Vietnam Journal of Science and Technology 54, n^o 2 (12 avril 2016) : 276. http://dx.doi.org/10.15625/0866-708x/54/2/6233.

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The paper proposes a theorem to assert the arbitrarily good robustness of the fully actuated mechanical system controlled by the adaptive feedback linearization controller. The fully actuated system to be controlled is considerately perturbed by input disturbances and contains constant uncertain parameters in its Euler-Lagrange forced model. It is shown in this paper that independent of input disturbances the adaptive feedback linearization controller with appropriately chosen parameters will drive the output of controlled systems to the desired trajectory for any arbitrary precision. The adaptive controller is applied to the two-link planar elbow arm robot with unknown mass of the end-effector of second link and input torque noises caused by the viscous friction forces and Coulomb friction terms. Simulation results show that the arbitrary precision of the tracking errors always are guaranteed.

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Xu, F. Y., et B. Z. Cao. « An Improvement for Calculating Precision of Arbitrary Groove Guide ». Journal of Electromagnetic Waves and Applications 19, n^o 3 (janvier 2005) : 341–53. http://dx.doi.org/10.1163/1569393054139624.

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Milton, Gareth E., et Jay Katupitiya. « Fabrication of arbitrary precision micro profiles by nano-grinding ». International Journal of Nanomanufacturing 8, n^o 3 (2012) : 231. http://dx.doi.org/10.1504/ijnm.2012.047030.

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Thomaz, Lucas A., Pedro A. A. Assuncao, Luis M. N. Tavora et Sergio M. M. de Faria. « Integer DCT Approximation With Arbitrary Size and Adjustable Precision ». IEEE Signal Processing Letters 27 (2020) : 965–69. http://dx.doi.org/10.1109/lsp.2020.2998362.

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FILIPICH, C. P., et M. B. ROSALES. « ARBITRARY PRECISION FREQUENCIES OF A FREE RECTANGULAR THIN PLATE ». Journal of Sound and Vibration 230, n^o 3 (février 2000) : 521–39. http://dx.doi.org/10.1006/jsvi.1999.2629.

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Ryšavý, M. « MISHA - a system for calculations with arbitrary arithmetic precision ». Computer Physics Communications 47, n^o 2-3 (novembre 1987) : 351–59. http://dx.doi.org/10.1016/0010-4655(87)90120-2.

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Dzhambov, Velichko. « High precision computing of definite integrals with .net framework c# and x-mpir ». Cybernetics and Information Technologies 14, n^o 1 (1 mars 2014) : 172–82. http://dx.doi.org/10.2478/cait-2014-0014.

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Abstract This paper concerns high precision numerical computing of definite integrals in a specific environment, namely .NET Framework. The work is a part of a series, tracing the progress of creating tools for high precision computations in this environment and may be considered as a continuation, in this direction, of the beginning, described in [15], that includes special function calculations with arbitrary precision. Some of the methods used are described. The results are clearly illustrated with the help of an application, purposefully created, using the current state-of-the-art library being created for realization of functions and numerical methods of arbitrary precision in a given environment.

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Ahmadi, Hamed, et Chen-Fu Chiang. « Quantum phase estimation with arbitrary constant-precision phase shift operators ». Quantum Information and Computation 12, n^o 9&10 (septembre 2012) : 864–75. http://dx.doi.org/10.26421/qic12.9-10-9.

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While Quantum phase estimation (QPE) is at the core of many quantum algorithms known to date, its physical implementation (algorithms based on quantum Fourier transform (QFT) ) is highly constrained by the requirement of high-precision controlled phase shift operators, which remain difficult to realize. In this paper, we introduce an alternative approach to approximately implement QPE with arbitrary constant-precision controlled phase shift operators. The new quantum algorithm bridges the gap between QPE algorithms based on QFT and Kitaev's original approach. For approximating the eigenphase precise to the nth bit, Kitaev's original approach does not require any controlled phase shift operator. In contrast, QPE algorithms based on QFT or approximate QFT require controlled phase shift operators with precision of at least Pi/2n. The new approach fills the gap and requires only arbitrary constant-precision controlled phase shift operators. From a physical implementation viewpoint, the new algorithm outperforms Kitaev's approach.

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Liptaj, Andrej. « HIGHER ACCURACY ORDER IN DIFFERENTIATION-BY-INTEGRATION ». Mathematical Modelling and Analysis 26, n^o 2 (26 mai 2021) : 304–17. http://dx.doi.org/10.3846/mma.2021.13119.

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In this text explicit forms of several higher precision order kernel functions (to be used in the differentiation-by-integration procedure) are given for several derivative orders. Also, a system of linear equations is formulated which allows to construct kernels with an arbitrary precision for an arbitrary derivative order. A computer study is realized and it is shown that numerical differentiation based on higher precision order kernels performs much better (w.r.t. errors) than the same procedure based on the usual Legendre-polynomial kernels. Presented results may have implications for numerical implementations of the differentiation-by-integration method.

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Dena, Ángeles, Marcos Rodríguez, Sergio Serrano et Roberto Barrio. « High-Precision Continuation of Periodic Orbits ». Abstract and Applied Analysis 2012 (2012) : 1–12. http://dx.doi.org/10.1155/2012/716024.

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Obtaining periodic orbits of dynamical systems is the main source of information about how the orbits, in general, are organized. In this paper, we extend classical continuation algorithms in order to be able to obtain families of periodic orbits with high-precision. These periodic orbits can be corrected to get them with arbitrary precision. We illustrate the method with two important classical Hamiltonian problems.

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WITTIG, ALEXANDER, et MARTIN BERZ. « COMPUTATION OF HIGH-ORDER MAPS TO MULTIPLE MACHINE PRECISION ». International Journal of Modern Physics A 24, n^o 05 (20 février 2009) : 1019–39. http://dx.doi.org/10.1142/s0217751x09044474.

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The Beam Dynamics simulation package in COSY INFINITY is built upon a differential algebra data type. With it, it is possible to compute transfer maps or arbitrary systems to arbitrary order. However, this data type is limited by the precision of the underlying floating point number model provided by the computer processor. We will present a method to extend the effective precision of the calculations based purely on standard floating point operations. Those algorithms are then integrated into the differential algebra data type to efficiently extend the available precision, without unnecessarily affecting overall efficiency. To that effect, the precision of each coefficient is adjusted automatically during the calculation. We will then proceed to show the effectiveness of our implementation by calculating high precision maps of combinations of homogeneous dipole segments, for which the exact results are known, and comparing the high precision coefficients with the results produced by the traditional COSY beam physics package.

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Yang, Mo, Zhong Da Guo et Zhi Qiang Yang. « Arbitrary Curvature Radius of the Optical Parts Precision Polishing Technology ». Advanced Materials Research 683 (avril 2013) : 589–94. http://dx.doi.org/10.4028/www.scientific.net/amr.683.589.

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This paper puts forward a kind of magnetorheological polishing technology of arbitrary curvature radius spherical optical parts and the mechanical structure of its supporting equipment. By changing the position of the intersection point of the spindle unit and pendulum shaft device in the space, it can achieve high quality and rapid processing of an arbitrary curvature radius of the spherical optical parts. The wheel-head structure of our equipment is an endless belt structure. The magnetorheological fluids are added to the endless belt, and the wheel-head structure 15 is powered. Then, it will form a Bingham on the endless belt with which the surface of the processed optical parts contact. At last, it will achieve precision flexible polishing process ultimately. A simple mechanical structure design and breakthrough processing method are used in the equipment and the complete processing technology, which can achieve flexible polishing of large-diameter spherical (or plane) optical components with any radius. The machining accuracy is less than 1nm, achieving the requirements of the ultra-smooth surface.

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Benz, S. P., P. D. Dresselhaus, C. J. Burroughs et N. F. Bergren. « Precision Measurements Using a 300 mV Josephson Arbitrary Waveform Synthesizer ». IEEE Transactions on Applied Superconductivity 17, n^o 2 (juin 2007) : 864–69. http://dx.doi.org/10.1109/tasc.2007.898138.

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Duque, Daniel, Pep Español et Jaime Arturo de la Torre. « Extending linear finite elements to quadratic precision on arbitrary meshes ». Applied Mathematics and Computation 301 (mai 2017) : 201–13. http://dx.doi.org/10.1016/j.amc.2016.12.010.

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'Aurizio, Jacopo. « Refinements of the Shafer-Fink inequality of arbitrary uniform precision ». Mathematical Inequalities & ; Applications, n^o 4 (2014) : 1487–98. http://dx.doi.org/10.7153/mia-17-109.

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Varin, Victor Petrovich. « Integration of ODEs on Riemann surfaces with an arbitrary precision ». Keldysh Institute Preprints, n^o 1 (2019) : 1–24. http://dx.doi.org/10.20948/prepr-2019-1.

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Fuda, Toru. « Convergence Conditions of Mixed States and their von Neumann Entropy in Continuous Quantum Measurements ». Open Systems & ; Information Dynamics 21, n^o 04 (décembre 2014) : 1450010. http://dx.doi.org/10.1142/s1230161214500103.

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By carrying out appropriate continuous quantum measurements with a family of projection operators, a unitary channel can be approximated in an arbitrary precision in the trace norm sense. In particular, the quantum Zeno effect is described as an application. In the case of an infinite dimension, although the von Neumann entropy is not necessarily continuous, the difference of the entropies between the states, as mentioned above, can be made arbitrarily small under some conditions.

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Morishige, Koichi, Shingo Ishizuka et Yoshimi Takeuchi. « Development of Tool Fabrication CAD/CAM for Conicoid End Mill ». International Journal of Automation Technology 1, n^o 2 (5 novembre 2007) : 128–35. http://dx.doi.org/10.20965/ijat.2007.p0128.

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This study deals with new practical fabrication of end mills based on 3D-CAD/CAM. End mills with arbitrary shapes generally difficult to produce are useful in upgrading machining accuracy and efficiency. Our tool fabrication CAD/CAM potentially produces end mills with arbitrarily shaped cutting edge. In order to make them practical, we developed a way to design the cutting edge shape and NC data generation for a 5-axis controlled tool grinding machine. The resulting system enables produces practical, arbitrarily shaped end mills with shape precision comparable to their commercially available counterparts.

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Pang, Qilong, Liangjie Kuang, Youlin Xu et Xiang Dai. « Study on the extraction and reconstruction of arbitrary frequency topography from precision machined surfaces ». Proceedings of the Institution of Mechanical Engineers, Part B : Journal of Engineering Manufacture 233, n^o 7 (24 septembre 2018) : 1772–80. http://dx.doi.org/10.1177/0954405418802307.

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This article presents an extraction and reconstruction method for arbitrary two-dimensional and three-dimensional frequency features in precision machined surfaces. A combination of power spectrum density and continuous wavelet transform is used to analyze the potassium dihydrogen phosphate crystal surface topography. All frequencies involved in sampling area of measuring instrument are distinguished by power spectrum density method. Compared to discrete wavelet transform used to decompose frequency features, continuous wavelet transform method can extract and reconstruct two-dimensional profile and three-dimensional topography of arbitrary frequency features from original precision machined surfaces. Analysis results show that amplitude and distribution of different frequency features in two-dimensional profile or three-dimensional surface topography are fully restored by continuous wavelet transform. The effects of different factors in machining process on precision machined surface topography may be discovered. Furthermore, the extraction and reconstruction method is generally applicable for the analysis of all precision machined surfaces.

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Ait Said, Noureddine, Mounir Benabdenbi et Katell Morin-Allory. « Arbitrary Reduced Precision for Fine-grained Accuracy and Energy Trade-offs ». Microelectronics Reliability 120 (mai 2021) : 114099. http://dx.doi.org/10.1016/j.microrel.2021.114099.

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LEI, Yuanwu, Yong DOU et Jie ZHOU. « FPGA-Specific Custom VLIW Architecture for Arbitrary Precision Floating-Point Arithmetic ». IEICE Transactions on Information and Systems E94-D, n^o 11 (2011) : 2173–83. http://dx.doi.org/10.1587/transinf.e94.d.2173.

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Chalin, Patrice. « JML Support for Primitive Arbitrary Precision Numeric Types : Definition and Semantics. » Journal of Object Technology 3, n^o 6 (2004) : 57. http://dx.doi.org/10.5381/jot.2004.3.6.a3.

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Haurie, X., et G. W. Roberts. « Arbitrary-precision signal generation for mixed-signal built-in-self-test ». IEEE Transactions on Circuits and Systems II : Analog and Digital Signal Processing 45, n^o 11 (1998) : 1425–32. http://dx.doi.org/10.1109/82.735354.

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Wyffels, Kevin, et Mark Campbell. « Precision Tracking via Joint Detailed Shape Estimation of Arbitrary Extended Objects ». IEEE Transactions on Robotics 33, n^o 2 (avril 2017) : 313–32. http://dx.doi.org/10.1109/tro.2016.2630058.

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Li, He, James J. Davis, John Wickerson et George A. Constantinides. « architect : Arbitrary-Precision Hardware With Digit Elision for Efficient Iterative Compute ». IEEE Transactions on Very Large Scale Integration (VLSI) Systems 28, n^o 2 (février 2020) : 516–29. http://dx.doi.org/10.1109/tvlsi.2019.2945257.

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Yang, Daniel C. H., et Alex D. Golub. « Precision trajectory generation for CNC milling of arbitrary contours and surfaces ». International Journal of Machine Tools and Manufacture 34, n^o 7 (octobre 1994) : 1005–18. http://dx.doi.org/10.1016/0890-6955(94)90031-0.

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Johansson, Fredrik. « Computing the Lambert W function in arbitrary-precision complex interval arithmetic ». Numerical Algorithms 83, n^o 1 (18 février 2019) : 221–42. http://dx.doi.org/10.1007/s11075-019-00678-x.

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Stockburger, Jürgen T., et C. H. Mak. « Stochastic Liouvillian algorithm to simulate dissipative quantum dynamics with arbitrary precision ». Journal of Chemical Physics 110, n^o 11 (15 mars 1999) : 4983–85. http://dx.doi.org/10.1063/1.478396.

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Cheng, Kuo-Hsing, Kai-Wei Hong, Chi-Hsiang Chen et Jen-Chieh Liu. « A High Precision Fast Locking Arbitrary Duty Cycle Clock Synchronization Circuit ». IEEE Transactions on Very Large Scale Integration (VLSI) Systems 19, n^o 7 (juillet 2011) : 1218–28. http://dx.doi.org/10.1109/tvlsi.2010.2049387.

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Fasi, Massimiliano, et Nicholas J. Higham. « An Arbitrary Precision Scaling and Squaring Algorithm for the Matrix Exponential ». SIAM Journal on Matrix Analysis and Applications 40, n^o 4 (janvier 2019) : 1233–56. http://dx.doi.org/10.1137/18m1228876.

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Revol, Nathalie, et Fabrice Rouillier. « Motivations for an Arbitrary Precision Interval Arithmetic and the MPFI Library ». Reliable Computing 11, n^o 4 (août 2005) : 275–90. http://dx.doi.org/10.1007/s11155-005-6891-y.

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KARASAWA, TOKISHIRO, MASANAO OZAWA, JULIO GEA-BANACLOCHE et KAE NEMOTO. « QUANTUM PRECISION LIMITS FOR ANY IMPLEMENTATION OF SINGLE QUBIT GATES UNDER CONSERVATION LAWS ». International Journal of Quantum Information 06, supp01 (juillet 2008) : 701–6. http://dx.doi.org/10.1142/s0219749908003980.

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A quantum gate is implemented by control interactions between qubits and their ancilla system. It has been shown that the control interactions have possibilities to induce the dynamical decoherence on the qubits if an additive conservation law is assumed in the interactions and the ancilla system is finite. This decoherece put the precision limit on the gate, which cannot be removed from the qubit by optimizing the interaction and the initialization of the ancilla system. In this paper, we give the outline of investigating the precision limit which is formulated by the lower bound of the gate infidelity, one minus the squared fidelity, for an arbitrary self-adjoint gate on a single qubit. We show rigorous lower bounds in terms of the variance of the conserved quantity and a simple geometrical relation between the conservation law to be assumed and the gates to be implemented. We also comment on another approach to provide the precision limit for an arbitrary single qubit gate under a conservation law.

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Wang, Yi-Han, Nathan W. C. Leigh, Bin Liu et Rosalba Perna. « SpaceHub : A high-performance gravity integration toolkit for few-body problems in astrophysics ». Monthly Notices of the Royal Astronomical Society 505, n^o 1 (30 avril 2021) : 1053–70. http://dx.doi.org/10.1093/mnras/stab1189.

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ABSTRACT We present the open source few-body gravity integration toolkit SpaceHub. SpaceHub offers a variety of algorithmic methods, including the unique algorithms AR-Radau, AR-Sym6, AR-ABITS, and AR-chain+ which we show outperform other methods in the literature and allow for fast, precise, and accurate computations to deal with few-body problems ranging from interacting black holes to planetary dynamics. We show that AR-Sym6 and AR-chain+, with algorithmic regularization, chain algorithm, active round-off error compensation and a symplectic kernel implementation, are the fastest and most accurate algorithms to treat black hole dynamics with extreme mass ratios, extreme eccentricities, and very close encounters. AR-Radau, the first regularized Radau integrator with round off error control down to 64 bits floating point machine precision, has the ability to handle extremely eccentric orbits and close approaches in long-term integrations. AR-ABITS, a bit efficient arbitrary precision method, achieves any precision with the least CPU cost compared to other open source arbitrary precision few-body codes. With the implementation of deep numerical and code optimization, these new algorithms in SpaceHub prove superior to other popular high precision few-body codes in terms of performance, accuracy, and speed.

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Lu, Hai Xiang, Jing Hua Diao et Zeng Zhi Li. « Research on the Selecting Control Sections of Internal Force Envelope by Simulation ». Applied Mechanics and Materials 226-228 (novembre 2012) : 1467–71. http://dx.doi.org/10.4028/www.scientific.net/amm.226-228.1467.

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The simulation optimization of internal force envelope in plane bar structure subjected to complex moving loads, including arbitrary concentrated force, concentrated couple, linearly distributed force and etc, was mainly discussed. By means of Vsap2011, the plane bar structure analyzing software, the effects of internal force envelope’s control sections on the solving precision of internal force envelope were analyzed. The research had reached to some important conclusions that in order to the obtain higher solving precision of internal force envelope, the element passed by moving loads should be divided by steps; more than enough dividing points should be inserted between load acting points for the element arbitrarily distributed with live loads; the element without any loads should be divided by defined interval when its both ends are rigid-jointed, while it should not be divided when its single or both ends are hinged-jointed.

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Novokshonov, A. K. « Performance analysis of arithmetic algorithms implemented in C++ and Python programming languages ». PROBLEMS IN PROGRAMMING, n^o 2-3 (juin 2016) : 026–31. http://dx.doi.org/10.15407/pp2016.02-03.026.

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This paper presents the results of the numerical experiment, which aims to clarify the actual performance of arithmetic algorithms implemented in C ++ and Python programming languages using arbitrary precision arithmetic. "Addition machine" has been chosen as a mathematical model for integer arithmetic algorithms. "Addition machine" is a mathematical abstraction, introduced by R. Floyd and D. Knuth. The essence of "addition machine" is the following: using only operations of addition, subtraction, comparison, assignment and a limited number of registers it is possible to calculate more complex operations such as finding the residue modulo, multiplication, finding the greatest common divisor, exponentiation modulo with reasonable computational efficiency. One of the features of this implementation is the use of arbitrary precision arithmetic, which may be useful in cryptographic algorithms.

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Lin, Dongfeng, Danyang Li, Yiping Cui, Tao Zhang, Fanchao Meng, Xiaoting Zhao, Jinmin Ding et Sheng Liang. « Machine learning-based error compensation for high precision laser arbitrary beam splitting ». Optics and Lasers in Engineering 160 (janvier 2023) : 107245. http://dx.doi.org/10.1016/j.optlaseng.2022.107245.

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Amore, Paolo. « Computing the solutions of the van der Pol equation to arbitrary precision ». Physica D : Nonlinear Phenomena 435 (juillet 2022) : 133279. http://dx.doi.org/10.1016/j.physd.2022.133279.

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Articles de revues sur le sujet « Arbitrary precision »

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