A Low-Memory Lanczos Method with Rational Krylov Compression for Matrix Functions: A low-memory Lanczos method with rational Krylov compression for matrix functions

Authors: Angelo A. Casulli, Igor Simunec

Source: SIAM Journal on Scientific Computing. 47:A1358-A1382

Subject Terms: Numerical computation of matrix exponential and similar matrix functions, Computational methods for sparse matrices, matrix function, 65F60, 65F50, Mathematics - Numerical Analysis, rational Krylov, low memory

File Description: application/xml

Access URL: http://arxiv.org/abs/2403.04390

Mixed-Precision Paterson–Stockmeyer Method for Evaluating Polynomials of Matrices: Mixed-precision Paterson-Stockmeyer method for evaluating polynomials of matrices

Authors: Xiaobo Liu

Source: SIAM Journal on Matrix Analysis and Applications. 46:811-835

Subject Terms: Numerical computation of matrix exponential and similar matrix functions, mixed-precision algorithm, arbitrary-precision arithmetic, Roundoff error, Interval and finite arithmetic, matrix function, FOS: Mathematics, 15A16, 65F60, 65G50, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Paterson-Stockmeyer method, rounding error analysis, matrix polynomial

File Description: application/xml

Access URL: http://arxiv.org/abs/2312.17396

Computing Functions of Symmetric Hierarchically Semiseparable Matrices: Computing functions of symmetric hierarchically semiseparable matrices

Authors: Angelo A. Casulli, Daniel Kressner, Leonardo Robol

Source: SIAM Journal on Matrix Analysis and Applications. 45:2314-2338

Subject Terms: Numerical computation of matrix exponential and similar matrix functions, hierarchically semiseparable, FOS: Mathematics, 65F60, 15B99, functions of matrices, Special matrices, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), rational Krylov

File Description: application/xml; application/pdf

Access URL: http://arxiv.org/abs/2402.17369
https://epubs.siam.org/doi/10.1137/24M1642354
https://doi.org/10.1137/24m1642354
https://hdl.handle.net/11568/1293575

A Simple GPU Implementation of Spectral-Element Methods for Solving 3D Poisson Type Equations on Rectangular Domains and Its Applications: A simple GPU implementation of spectral-element methods for solving 3D Poisson type equations on rectangular domains and its applications

Authors: Liu, Xinyu, Shen, Jie, Zhang, Xiangxiong

Source: Communications in Computational Physics. 36:1157-1185

Subject Terms: Numerical computation of matrix exponential and similar matrix functions, Finite difference methods for boundary value problems involving PDEs, FOS: Computer and information sciences, tensor matrix multiplication, rectangular domain, GPU, Parallel numerical computation, spectral element methods, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Direct numerical methods for linear systems and matrix inversion, direct solver, Computer Science - Distributed, Parallel, and Cluster Computing, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Spectral, collocation and related methods for boundary value problems involving PDEs, Mathematics - Numerical Analysis, Distributed, Parallel, and Cluster Computing (cs.DC), 3D Poisson equation, Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

File Description: application/xml

Access URL: http://arxiv.org/abs/2310.00226

Efficient third-order tensor-oriented directional splitting for exponential integrators

Authors: Cassini, Fabio

Source: ETNA - Electronic Transactions on Numerical Analysis. 60:520-540

Subject Terms: Numerical computation of matrix exponential and similar matrix functions, exponential integrators, $\mu$-mode product, directional splitting, $\varphi$-functions, Kronecker sum, Turing patterns, Graphic Processing Units, Kronecker sum, Multilinear algebra, tensor calculus, \( \varphi \)-functions, FOS: Mathematics, graphic processing units, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), directional splitting, Turing patterns, exponential integrators, \( \mu \)-mode product

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Access URL: http://arxiv.org/abs/2310.07551

Computing the Lyapunov operator φ-functions, with an application to matrix-valued exponential integrators: Computing the Lyapunov operator \(\varphi \)-functions, with an application to matrix-valued exponential integrators

Authors: Dongping Li, Yue Zhang, Xiuying Zhang

Source: Applied Numerical Mathematics. 182:330-343

Subject Terms: Numerical computation of matrix exponential and similar matrix functions, \( \varphi \)-functions, G.1.7, G.1.3, modified scaling and squaring method, Numerical Analysis (math.NA), Numerical methods for initial value problems involving ordinary differential equations, 01 natural sciences, 65F30, 65F10, 65L05, 15A60, Lyapunov operator, FOS: Mathematics, matrix-valued exponential integrators, Mathematics - Numerical Analysis, 0101 mathematics

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Access URL: http://arxiv.org/abs/2204.12976

Order reduction of matrix exponentials by proper orthogonal decomposition

Authors: Mohammad Dehghan Nayyeri, Mohammad Alinejadmofrad

Source: Results in Applied Mathematics, Vol 20, Iss, Pp 100401-(2023)

Subject Terms: Numerical computation of matrix exponential and similar matrix functions, low-rank approximation, 0209 industrial biotechnology, reduced order approximation, Numerical methods for low-rank matrix approximation, matrix compression, order reduction, 02 engineering and technology, Matrix exponential, Low-rank approximation, Proper orthogonal decomposition, Reduced order approximation, Numerical methods for initial value problems involving ordinary differential equations, matrix exponential, proper orthogonal decomposition, QA1-939, Order reduction, 0204 chemical engineering, Mathematics

File Description: application/xml

Access URL: https://zbmath.org/7786756
https://doi.org/10.1016/j.rinam.2023.100401
https://doaj.org/article/8a611a9c659e4003bd36a6433bac7062

Solving engineering models using hyperbolic matrix functions

Authors: Defez Candel, Emilio, Sastre, Jorge, Ibáñez González, Jacinto Javier, Peinado Pinilla, Jesús

Contributors: Escuela Técnica Superior de Ingeniería de Telecomunicación, Departamento de Sistemas Informáticos y Computación, Departamento de Matemática Aplicada, Departamento de Comunicaciones, Instituto Universitario de Telecomunicación y Aplicaciones Multimedia, Instituto Universitario de Matemática Multidisciplinar, Escuela Técnica Superior de Ingeniería de Caminos, Canales y Puertos, Escuela Técnica Superior de Ingeniería Informática, Instituto de Instrumentación para Imagen Molecular, Ministerio de Economía y Competitividad, Repositorio Institucional de la Universitat Politècnica de València Riunet

Source: RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Universitat Politècnica de València (UPV)
instname

Subject Terms: Numerical computation of matrix exponential and similar matrix functions, hyperbolic matrix functions, Hyperbolic matrix functions, Hermite matrix polynomial, 01 natural sciences, Initial-boundary value problems for second-order hyperbolic systems, Matrix exponential and similar functions of matrices, TEORIA DE LA SEÑAL Y COMUNICACIONES, CIENCIAS DE LA COMPUTACION E INTELIGENCIA ARTIFICIAL, Series expansion, 0101 mathematics, MATEMATICA APLICADA, LENGUAJES Y SISTEMAS INFORMATICOS, series expansion

File Description: application/pdf; application/xml

Access URL: https://riunet.upv.es/handle/10251/84125
http://www.sciencedirect.com/science/article/pii/S0307904X15005843
https://www.sciencedirect.com/science/article/abs/pii/S0307904X15005843
https://riunet.upv.es/handle/10251/84125
https://www.sciencedirect.com/science/article/pii/S0307904X15005843
https://hdl.handle.net/10251/84125
https://doi.org/10.1016/j.apm.2015.09.050

Solution of the delayed single degree of freedom system equation by exponential matrix method

Authors: SEZER, MEHMET, ÇEVİK, MEHMET, Bahsi, M. Mustafa

Source: Applied Mathematics and Computation. 242:444-453

Subject Terms: Numerical computation of matrix exponential and similar matrix functions, 2. Zero hunger, exponential collocation method, 0209 industrial biotechnology, Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations, Numerical methods for functional-differential equations, 02 engineering and technology, 0101 mathematics, time delay, single degree of freedom system, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/6574883
https://doi.org/10.1016/j.amc.2014.05.111
https://dblp.uni-trier.de/db/journals/amc/amc242.html#CevikBS14
https://www.sciencedirect.com/science/article/pii/S009630031400811X
http://www.sciencedirect.com/science/article/pii/S009630031400811X
https://avesis.deu.edu.tr/publication/details/13fac219-c556-4513-a215-aa2ac6cd0eea/oai

Method for calculating multiwave scattering by layered anisotropic media

Authors: Yuriy N. Belyayev

Source: Wave Motion. 99:102664

Subject Terms: Numerical computation of matrix exponential and similar matrix functions, Matrix exponential and similar functions of matrices, Wave scattering in solid mechanics, Numerical and other methods in solid mechanics, relative truncation error, 0103 physical sciences, diffraction of elastic waves, acoustic stresses, 01 natural sciences, Diffraction, scattering, matrix exponential

File Description: application/xml

Access URL: https://zbmath.org/7328388
https://doi.org/10.1016/j.wavemoti.2020.102664
https://www.sciencedirect.com/science/article/pii/S0165212520302948