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Shift-Invert Arnoldi's Method with Preconditioned Iterative Solves
SIAM Journal on Matrix Analysis and Applications, 2010The authors consider the computation of a few eigenvectors and the corresponding eigenvalues of a large sparse nonsymmetric matrix using the shift-invert Arnoldi method with and without implicit restarts. They extend the relaxation strategy of \textit{V. Simoncini} [SIAM J. Numer. Anal. 43, 1155--1174 (2005; Zbl 1093.65037)] to the implicitly restarted
Mélina A Freitag, Alastair Spence
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Multiple Explicitly Restarted Arnoldi Method for Solving Large Eigenproblems
SIAM Journal of Scientific Computing, 2005Summary: We propose a new approach for calculating some eigenpairs of large sparse non-Hermitian matrices. This method, called multiple explicitly restarted Arnoldi (MERAM), is particularly well suited for environments that combine different parallel programming paradigms.
Serge Petiton
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Laplacian Preconditioning for the Inverse Arnoldi Method
Communications in Computational Physics, 2015 Many physical processes are described by elliptic or parabolic partial differential equations. For linear stability problems associated with such equations, the inverse Laplacian provides a very effective preconditioner. In addition, it is also readily available in most scientific calculations in the form of a Poisson solver or an implicit diffusive ...
Laurette S. Tuckerman
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SIAM Journal on Matrix Analysis and Applications, 2014 The partial Schur factorization can be used to represent several eigenpairs of a matrix in a numerically robust way. Different adaptions of the Arnoldi method are often used to compute partial Schur factorizations.
Elias Jarlebring +2 more
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An extended shift-invert residual Arnoldi method
Computational and Applied Mathematics, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Su-Feng Yue, Jian-Jun Zhang 0002
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On a new variant of Arnoldi method for approximation of eigenpairs
Journal of Computational and Applied Mathematics, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bo Feng, Gang Wu
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A matrix analysis of Arnoldi and Lanczos methods
Numerische Mathematik, 1998The author presents a matrix analysis of the Arnoldi and Lanczos methods for approximating eigenpairs of a non-normal matrix. A new relation between the matrix representation of the two methods is defined to relate the corresponding eigenvalues and eigenvectors.
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Propagation of nonparaxial beams with a modified Arnoldi method
Optics Letters, 2001We have developed a modified Arnoldi method that includes a complex square-root approximation, which excels at modeling the propagation of highly diverging beams in various media. Simulations of one transverse dimensional beam with an ultranarrow width and of cylindrical Gaussian beams with various divergence angles reveal the strength of this ...
Q, Luo, C T, Law
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On Arnoldi Method Accelerating PageRank Computations
2010PageRank is a very important ranking algorithm in web information retrieval or search engine. We present Power method with Arnoldi acceleration for the computation of Pagerank vector, which can take the advantage of both Power method and Arnoldi process. The description and implementation of the new algorithm are discussed in detail.
Guo-Jian Yin, Jun-Feng Yin
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Using the Restricted-denominator Rational Arnoldi Method for Exponential Integrators [PDF]
SIAM Journal on Matrix Analysis and Applications, 2011 In this paper we investigate some practical aspects concerning the use of the restricted-denominator rational Arnoldi method for the computation of the core functions of exponential integrators for parabolic problems.
NOVATI, PAOLO
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