Improving Performance of Contour Integral-Based Nonlinear Eigensolvers with Infinite GMRES: Improving performance of contour integral-based nonlinear eigensolvers with infinite GMRES

Συγγραφείς: Yuqi Liu, Jose E. Roman, Meiyue Shao

Πηγή: SIAM Journal on Scientific Computing. 47:B595-B617

Θεματικοί όροι: Numerical solution of nonlinear eigenvalue and eigenvector problems, Numerical computation of eigenvalues and eigenvectors of matrices, infinite Arnoldi, contour integration, nonlinear eigenvalue problem, FOS: Mathematics, Krylov methods, companion linearization, Mathematics - Numerical Analysis, Numerical Analysis (math.NA)

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Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2403.19309
https://zbmath.org/8037158
https://doi.org/10.1137/24m1650375

Solving the quadratic eigenvalue problem expressed in non-monomial bases by the tropical scaling

Συγγραφείς: Chen, Hongjia, Wang, Teng, Zhang, Chun-Hua, Wang, Xiang

Πηγή: Advances in Computational Mathematics. 50

Θεματικοί όροι: Numerical solution of nonlinear eigenvalue and eigenvector problems, quadratic eigenvalue problem, tropical scaling, Taylor basis, Lagrange basis, block Kronecker linearization, backward error, Newton basis

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Σύνδεσμος πρόσβασης: https://zbmath.org/7964511
https://doi.org/10.1007/s10444-024-10214-8

NONLINEAR NUMERICS: Nonlinear numerics

Συγγραφείς: Doedel, Eusebius

Συνεισφορές: Thorin, Anders

Πηγή: International Journal of Bifurcation and Chaos. :2127-2143

Θεματικοί όροι: Chua's circuit, [PHYS.MECA.SOLID] Physics [physics]/Mechanics [physics]/Solid mechanics [physics.class-ph], Bifurcation theory for ordinary differential equations, homoclinic bifurcation, Josephson junctions, numerical bifurcation analysis, coupled Josephson junctions, [SPI.GCIV.STRUCT] Engineering Sciences [physics]/Civil Engineering/Structures, [SPI.GCIV.DV] Engineering Sciences [physics]/Civil Engineering/Dynamique, vibrations, 01 natural sciences, Global methods, including homotopy approaches to the numerical solution of nonlinear equations, Numerical solution of nonlinear eigenvalue and eigenvector problems, computational examples, Plant's model, ordinary differential equations, 0103 physical sciences, nonlinear equations, [SPI.MECA.VIBR] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Vibrations [physics.class-ph], [SPI.MECA.STRU] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Structural mechanics [physics.class-ph], bursting, 0101 mathematics, Numerical solution of eigenvalue problems involving ordinary differential equations, continuation, [SPI.MECA.GEME] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanical engineering [physics.class-ph], singular perturbation

Περιγραφή αρχείου: application/pdf; application/xml

Σύνδεσμος πρόσβασης: https://hal.archives-ouvertes.fr/hal-01634308/file/EJDA.pdf
https://zbmath.org/1217297
https://doi.org/10.1142/s0218127497001576

A note on finding roots of monotonic branching functions

Συγγραφείς: Ray Lawther

Πηγή: Communications in Numerical Methods in Engineering. 21:397-404

Θεματικοί όροι: numerical examples, monotonic, transcendental eigenvalue problems, 02 engineering and technology, root-finding, algorithms, 01 natural sciences, Numerical solution of nonlinear eigenvalue and eigenvector problems, 0203 mechanical engineering, branching, buckling, vibration, 0101 mathematics, root-counting

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/2207021
https://doi.org/10.1002/cnm.749
https://www.onlinelibrary.wiley.com/doi/pdf/10.1002/cnm.749
https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1002%2Fcnm.749

Nonlinear eigenvalue problems: a challenge for modern eigenvalue methods: Nonlinear eigenvalue problems: A challenge for modern eigenvalue methods

Συγγραφείς: Volker Mehrmann, Heinrich Voss

Πηγή: GAMM-Mitteilungen. 27:121-152

Θεματικοί όροι: Numerical solution of nonlinear eigenvalue and eigenvector problems, Arnoldi method, rational eigenvalue problems, linearization, Jacobi-Davidson method, numerical results, 0101 mathematics, 01 natural sciences, Krylov subspace method

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://tore.tuhh.de/bitstream/11420/63/1/rep83.pdf
https://tore.tuhh.de/bitstream/11420/63/1/rep83.pdf
http://tubdokservice.tub.tuhh.de/redirect.php?id=2005/116/pdf/rep83.pdf
https://core.ac.uk/display/22871870
https://www.mat.tuhh.de/forschung/rep/rep83.pdf
https://onlinelibrary.wiley.com/doi/abs/10.1002/gamm.201490007
https://www.mat.tu-harburg.de/forschung/rep/rep83.pdf

MULTIGRID-CONJUGATE GRADIENT TYPE METHODS FOR REACTION–DIFFUSION SYSTEMS: Multigrid-conjugate gradient type methods for reaction-diffusion systems.

Συγγραφείς: S.-L. Chang, C.-S. Chien, H. S. Chen

Πηγή: International Journal of Bifurcation and Chaos. 14:3587-3605

Θεματικοί όροι: Numerical methods for eigenvalue problems for boundary value problems involving PDEs, Multigrid methods, domain decomposition for boundary value problems involving PDEs, finite differences, 4. Education, nonlinear elliptic eigenvalue problem, multigrid methods, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, numerical results, GMRES, \(W\)-cycle, continuation methods, algorithms, 01 natural sciences, Global methods, including homotopy approaches to the numerical solution of nonlinear equations, Numerical solution of nonlinear eigenvalue and eigenvector problems, Reaction-diffusion systems, Reaction-diffusion equations, Bi-CGSTAB, domain decomposition for initial value and initial-boundary value problems involving PDEs, nearly singular systems, Finite difference methods for initial value and initial-boundary value problems involving PDEs, bifurcation, \(V\)-cycle, 0101 mathematics

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://dblp.uni-trier.de/db/journals/ijbc/ijbc14.html#ChangCC04
http://ui.adsabs.harvard.edu/abs/2004IJBC...14.3587C/abstract
https://www.worldscientific.com/doi/10.1142/S0218127404011466
http://faculty.stust.edu.tw/~slchang/paper/15090625.pdf

An Arnoldi Method for Nonlinear Eigenvalue Problems: An Arnoldi method for nonlinear eigenvalue problems

Συγγραφείς: Voß, Heinrich

Πηγή: BIT Numerical Mathematics. 44:387-401

Θεματικοί όροι: Nichtlineares Eigenwertproblem, Inversion, Systems arising from the discretization of structural vibration problems, 01 natural sciences, Numerical solution of nonlinear eigenvalue and eigenvector problems, iterative projection method, numerical example, shift-and-invert Arnoldi method, residual inverse iteration, Projektionsverfahren, damped vibrations of a structure, Mathematik, nonlinear eigenvalue problem, 0101 mathematics, Eigenvalues, eigenvectors, rational eigenvalue problem

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://tore.tuhh.de/bitstream/11420/147/1/rep56.pdf
https://portal.dnb.de/opac.htm?method=simpleSearch&cqlMode=true&query=idn%3D1048408353
https://tore.tuhh.de/bitstream/11420/147/1/rep56.pdf
https://link.springer.com/article/10.1023%2FB%3ABITN.0000039424.56697.8b
https://tore.tuhh.de/handle/11420/147
https://d-nb.info/1048408353/34

Inverse power and Durand-Kerner iterations for univariate polynomial root-finding

Συγγραφείς: BINI, DARIO ANDREA, GEMIGNANI, LUCA, PAN V. Y.

Πηγή: Computers & Mathematics with Applications. 47:447-459

Θεματικοί όροι: inverse power iteration, algorithm, polynomial root-finding, generalized companion matrix, 01 natural sciences, Real polynomials: location of zeros, Generalized companion matrices, Numerical solution of nonlinear eigenvalue and eigenvector problems, Computational Mathematics, Matrix methods for root-finding, Computational Theory and Mathematics, Polynomial root-finding, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), Weierstrass (Durand-Kerner) algorithm, Modelling and Simulation, matrix methods, Higher-order root-finders, Computational aspects of field theory and polynomials, eigenvalue, Numerical computation of solutions to single equations, 0101 mathematics, Inverse power iteration, numerical experiments

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/2075472
https://doi.org/10.1016/s0898-1221(04)90037-5
https://arpi.unipi.it/handle/11568/202085
http://www.sciencedirect.com/science/article/pii/S0898122104900375
https://www.sciencedirect.com/science/article/pii/S0898122104900375
https://hdl.handle.net/11568/202085

A MULTIGRID-LANCZOS ALGORITHM FOR THE NUMERICAL SOLUTIONS OF NONLINEAR EIGENVALUE PROBLEMS: A multigrid-Lanczos algorithm for the numerical solutions of nonlinear eigenvalue problems.

Συγγραφείς: C.-S. Chien, S.-L. Chang

Πηγή: International Journal of Bifurcation and Chaos. 13:1217-1228

Θεματικοί όροι: Bifurcations in context of PDEs, Numerical methods for eigenvalue problems for boundary value problems involving PDEs, convergence, Lanczos method, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, nonlinear elliptic eigenvalue problems, Stability and convergence of numerical methods for boundary value problems involving PDEs, singular points, numerical results, 01 natural sciences, Global methods, including homotopy approaches to the numerical solution of nonlinear equations, Numerical solution of nonlinear eigenvalue and eigenvector problems, continuation method, bifurcation, minimal residual algorithm, 0101 mathematics, Multigrid method

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/2141855
https://doi.org/10.1142/s0218127403007175

On the construction of a Jacobi matrix from its mixed-type eigenpairs

Συγγραφείς: Lei Zhang, Zhen-yun Peng, Xi-Yan Hu

Πηγή: Linear Algebra and its Applications. 362:191-200

Θεματικοί όροι: numerical examples, Numerical Analysis, algorithm, reconstruction, Algebra and Number Theory, Eigenvalue, Numerical solutions to inverse eigenvalue problems, inverse eigenvalue problem, 01 natural sciences, Numerical solution of nonlinear eigenvalue and eigenvector problems, Jacobi matrix, Inverse eigenvalue problem, Discrete Mathematics and Combinatorics, Geometry and Topology, 0101 mathematics, Eigenvectors

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://www.sciencedirect.com/science/article/abs/pii/S0024379502004883
https://www.sciencedirect.com/science/article/pii/S0024379502004883

On the behaviour of the ANM continuation in the presence of bifurcations

Συγγραφείς: Baguet, Sébastien, Cochelin, Bruno

Συνεισφορές: Rosu, Elena

Πηγή: Communications in Numerical Methods in Engineering. 19:459-471

Θεματικοί όροι: Numerical solution of nonlinear eigenvalue and eigenvector problems, series convergence, power series expansions, asymptotic-numerical-method, 0203 mechanical engineering, bifurcation, [SPI.MECA.STRU] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Structural mechanics [physics.class-ph], 02 engineering and technology, 0101 mathematics, continuation, 01 natural sciences, Global methods, including homotopy approaches to the numerical solution of nonlinear equations

Περιγραφή αρχείου: application/pdf; application/xml

Σύνδεσμος πρόσβασης: https://hal.archives-ouvertes.fr/hal-00088346/file/SBBC.pdf
https://hal.science/hal-00088346v1/document
https://hal.science/hal-00088346v1
https://doi.org/10.1002/cnm.605
https://zbmath.org/1958249
https://doi.org/10.1002/cnm.605
https://hal.archives-ouvertes.fr/hal-00088346/document
https://onlinelibrary.wiley.com/doi/abs/10.1002/cnm.605
https://hal.archives-ouvertes.fr/hal-00088346

Indication of a stability loss in the continuation of invariant subspaces

Συγγραφείς: Vladimír Janovský, Ondřej Liberda

Πηγή: Mathematics and Computers in Simulation. 61:517-524

Θεματικοί όροι: steady states, Cayley transform, stability analysis, 01 natural sciences, Global methods, including homotopy approaches to the numerical solution of nonlinear equations, predictor-corrector algorithm, Numerical solution of nonlinear eigenvalue and eigenvector problems, continuation method, preconditioning, parameter-dependent nonlinear system bifurcation, subspace iterations, 0101 mathematics, invariant subspaces, pathfollowing

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/1882289
https://doi.org/10.1016/s0378-4754(02)00101-5
https://EconPapers.repec.org/RePEc:eee:matcom:v:61:y:2003:i:3:p:517-524
https://ideas.repec.org/a/eee/matcom/v61y2003i3p517-524.html
https://econpapers.repec.org/article/eeematcom/v_3a61_3ay_3a2003_3ai_3a3_3ap_3a517-524.htm
https://www.sciencedirect.com/science/article/pii/S0378475402001015
https://dblp.uni-trier.de/db/journals/mcs/mcs61.html#LiberdaJ03

Global monotone convergence of Newton iteration for a nonlinear eigen-problem

Συγγραφείς: I. Koltracht, Yung-Sze Choi, P. J. McKenna, N. Savytska

Πηγή: Linear Algebra and its Applications. 357:217-228

Θεματικοί όροι: Numerical Analysis, Algebra and Number Theory, fixed point problem, nonlinear eigen-problem, 01 natural sciences, Numerical solution of nonlinear eigenvalue and eigenvector problems, eigenvector, Newton algorithm, Newton method, global monotone convergence, Discrete Mathematics and Combinatorics, Stieltjes matrix, Geometry and Topology, 0101 mathematics, positive eigenvalue, Gross-Pitaevskii equation, Stieltjes matrices

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/1864779
https://doi.org/10.1016/s0024-3795(02)00383-x
https://www.sciencedirect.com/science/article/pii/S002437950200383X
https://www.sciencedirect.com/science/article/abs/pii/S002437950200383X

Free and forced vibrations of trusses by Fourier decomposition, and homotopy methods for nonlinear matrix eigenvalue problems: Free and forced vibrations of trusses by Fourier decomposition, and homotopy methods for nonlinear matrix eigenvalue problems. II: Properties and supplements

Συγγραφείς: E. Adams, Michael Plum

Πηγή: Journal of Mathematical Analysis and Applications. 275:333-353

Θεματικοί όροι: separation of variables, Applied Mathematics, elastic frames, 02 engineering and technology, 01 natural sciences, Numerical solution of nonlinear eigenvalue and eigenvector problems, clamping, free vibrations, Vibrations in dynamical problems in solid mechanics, 0203 mechanical engineering, nonlinear matrix eigenvalue problems, Fourier decomposition, Spectral and related methods applied to problems in solid mechanics, frequency domain method, eigensolutions, beams, Rods (beams, columns, shafts, arches, rings, etc.), 0101 mathematics, homotopy methods, spatial vibration methods, Analysis

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://www.sciencedirect.com/science/article/pii/S0022247X02003554
https://www.sciencedirect.com/science/article/pii/S0022247X02003554#!
https://www.sciencedirect.com/science/article/pii/S0022247X02003566
https://www.sciencedirect.com/science/article/abs/pii/S0022247X02003566

Descent Iterations for Improving Approximate Eigenpairs of Polynomial Eigenvalue Problems with General Complex Matrices: Descent iterations for improving approximate eigenpairs of polynomial eigenvalue problems with general complex matrices

Συγγραφείς: K. Ishihara

Πηγή: Computing. 68:239-254

Θεματικοί όροι: Numerical computation of eigenvalues and eigenvectors of matrices, Numerical solution of nonlinear eigenvalue and eigenvector problems, numerical examples, generalized damped Newton method, convergence, descent iteration, polynomial eigenvalue problem, generalized damped Gauss-Newton method, 0101 mathematics, 01 natural sciences

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/1798912
https://doi.org/10.1007/s00607-001-1435-8
https://link.springer.com/article/10.1007%2Fs00607-001-1435-8
https://dblp.uni-trier.de/db/journals/computing/computing68.html#Ishihara02

N Roots of the Secular Equation in O(N) Operations: \(N\) roots of the secular equation in \(O(N)\) operations

Συγγραφείς: Achi Brandt, Oren E. Livne

Πηγή: SIAM Journal on Matrix Analysis and Applications. 24:439-453

Θεματικοί όροι: Numerical computation of eigenvalues and eigenvectors of matrices, multilevel algorithm, discontinuous kernel softening, symmetric eigenvalue problems, secular equation, root-search, singular value decomposition, Parallel numerical computation, numerical results, integral transforms, 01 natural sciences, divide and concquer method, Numerical solution of nonlinear eigenvalue and eigenvector problems, fast multilevel summation, Complexity and performance of numerical algorithms, symmetric tridiagonal eigenbasis solvers, constrained least-squares problems, 0101 mathematics, parallel computation, Numerical methods for integral transforms

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/1848600
https://doi.org/10.1137/s0895479801383695
https://dblp.uni-trier.de/db/journals/siammax/siammax24.html#LivneB02
https://locus.siam.org/doi/abs/10.1137/S0895479801383695
https://epubs.siam.org/doi/abs/10.1137/S0895479801383695

A variational method for eigenvalue problems nonlinearly dependent on the spectral parameter: A variational method for eigenvalue problems nonlinearly dependent on the spectral parameter.

Συγγραφείς: Andrushkiw, RI, Slastikov, VV

Πηγή: Nonlinear Analysis: Theory, Methods & Applications. 47:3561-3566

Θεματικοί όροι: Numerical solution of nonlinear eigenvalue and eigenvector problems, 0211 other engineering and technologies, 02 engineering and technology, 0101 mathematics, 01 natural sciences, Equations and inequalities involving linear operators, with vector unknowns, Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones)

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://research-information.bris.ac.uk/en/publications/a-variational-method-for-eigenvalue-problems-nonlinearly-dependent-on-the-spectral-parameter(73ceb838-7cee-4801-ac04-383fef7cc28e).html
https://research-information.bristol.ac.uk/en/publications/a-variational-method-for-eigenvalue-problems-nonlinearly-dependent-on-the-spectral-parameter(73ceb838-7cee-4801-ac04-383fef7cc28e).html

Solving large nonlinear generalized eigenvalue problems from Density Functional Theory calculations in parallel: Solving large nonlinear generalized eigenvalue problems from density functional theory calculations in parallel

Συγγραφείς: Claus Bendtsen, Lars Bruno Hansen, O. H. Nielsen

Πηγή: Applied Numerical Mathematics. 37:189-199

Θεματικοί όροι: Numerical methods for eigenvalue problems for boundary value problems involving PDEs, self-consistent field, Condensed Matter - Materials Science, eigensolution, Completeness of eigenfunctions and eigenfunction expansions in context of PDEs, Materials Science (cond-mat.mtrl-sci), FOS: Physical sciences, Parallel numerical computation, 01 natural sciences, Atomic physics, Numerical solution of nonlinear eigenvalue and eigenvector problems, iterative Davidson algorithm, large eigenvalue problems, quantum mechanical ground state of electrons, nonlinear matrix eigenproblem, 0101 mathematics, parallel computation, density functional theory, PDEs in connection with quantum mechanics

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/pdf/cond-mat/0011107
http://arxiv.org/abs/cond-mat/0011107
https://www.sciencedirect.com/science/article/abs/pii/S0168927400000386#!
https://orbit.dtu.dk/en/publications/solving-large-nonlinear-generalized-eigenvalue-problems-from-density-functional-theory-calculations-in-parallel(415e2d0c-e471-4d24-aaf0-089e6598b558).html
https://www.sciencedirect.com/science/article/pii/S0168927400000386

On a New Homotopy Continuation Trajectory for Nonlinear Complementarity Problems: On a new homotopy continuation trajectory for nonlinear complementary problems.

Συγγραφείς: LiDuan, ZhaoYun-Bin

Πηγή: Mathematics of Operations Research. 26:119-146

Θεματικοί όροι: Numerical solution of nonlinear eigenvalue and eigenvector problems, Complementarity problems, continuation methods, homotopy continuation trajectories, strictly feasible condition, 0211 other engineering and technologies, 02 engineering and technology, Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/1677167
https://doi.org/10.1287/moor.26.1.119.10594
https://www.jstor.org/stable/3690439
https://pubsonline.informs.org/doi/abs/10.1287/moor.26.1.119.10594
https://dblp.uni-trier.de/db/journals/mor/mor26.html#ZhaoL01
http://web.mat.bham.ac.uk/Y.Zhao/My%20publication/MOR.pdf
https://ideas.repec.org/a/inm/ormoor/v26y2001i1p119-146.html
https://econpapers.repec.org/RePEc:inm:ormoor:v:26:y:2001:i:1:p:119-146
https://dl.acm.org/doi/10.5555/2780413.2780422

Iterative methods for large continuation problems

Συγγραφείς: Daniela Calvetti, Lothar Reichel

Πηγή: Journal of Computational and Applied Mathematics. 123:217-240

Θεματικοί όροι: numerical examples, symmetric matrix, Eigenvalue computation, Applied Mathematics, Numerical computation of solutions to systems of equations, eigenvectors, continuation problem, Bordering algorithm, continuation methods, algorithms, Turning point, 01 natural sciences, Global methods, including homotopy approaches to the numerical solution of nonlinear equations, turning point, Numerical solution of nonlinear eigenvalue and eigenvector problems, nonlinear parameter dependent problems, Computational Mathematics, Nonlinear system, iteration method, restarted block-Lanczos method, Bifurcation point, eigenvalue, singular point, 0101 mathematics, Path following

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://ui.adsabs.harvard.edu/abs/2000JCoAM.123..217C/abstract
https://www.sciencedirect.com/science/article/pii/S0377042700004052
https://dialnet.unirioja.es/servlet/articulo?codigo=700195