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M Popolizio, V Simoncini (2008)
Acceleration techniques for approximating the matrix exponential operatorSIAM J. Matrix Anal. Appl., 30
Y Saad, JR Chelikowsky, SM Shontz (2010)
Numerical methods for electronic structure calculations of materialsSIAM Rev., 52
A Ruhe (1984)
Rational Krylov sequence methods for eigenvalue computationLinear Algebra Appl., 58
J van den Eshof, M Hochbruck (2006)
Preconditioning Lanczos approximations to the matrix exponentialSIAM J. Sci. Comput., 27
GH Golub, G Meurant (1997)
Matrices, moments and quadrature. II. How to compute the norm of the error in iterative methodsBIT, 37
C Jagels, L Reichel (2011)
Recursion relations for the extended Krylov subspace methodLinear Algebra Appl., 434
M Hochbruck (1993)
Linear algebra for large scale and real-time applications
GH Golub, G Meurant (2010)
Matrices, Moments and Quadrature with Applications
V Faber, T Manteuffel (1984)
Necessary and sufficient conditions for the existence of a conjugate gradient methodSIAM J. Numer. Anal., 21
C Mertens, R Vandebril (2015)
Short recurrences for computing extended Krylov bases for Hermitian and unitary matricesNumer. Math., 131
C Jagels, L Reichel (2013)
The structure of matrices in rational Gauss quadratureMath. Comp., 82
S Güttel, L Knizhnerman (2013)
A black-box rational Arnoldi variant for Cauchy–Stieltjes matrix functionsBIT, 53
MH Gutknecht (1992)
A completed theory of the unsymmetric Lanczos process and related algorithms, part ISIAM J. Matrix Anal. Appl., 13
C Jagels, L Reichel (2009)
The extended Krylov subspace method and orthogonal Laurent polynomialsLinear Algebra Appl., 431
C Lanczos (1952)
Solutions of systems of linear equations by minimized iterationsJ. Res. Nat. Bur. Stand., 49
M Benzi, P Boito (2010)
Quadrature rule-based bounds for functions of adjacency matricesLinear Algebra Appl., 433
V Simoncini (2010)
Extended Krylov subspace for parameter dependent systemsAppl. Numer. Math., 60
Z Strakoš, P Tichý (2011)
On efficient numerical approximation of the bilinear form c∗A−1bSIAM J. Sci. Comput., 33
T Miyazaki (2012)
$\mathcal {O}(n)$O(n) methods in electronic structure calculationsRep. Prog. Phys., 75
E Estrada, D Higham (2010)
Network properties revealed through matrix functionsSIAM Rev., 52
GH Golub (1974)
Bounds for matrix momentsRocky Mt. J. Math., 4
JV Lambers (2009)
A spectral time-domain method for computational electrodynamicsAdv. Appl. Math. Mech., 1
JV Lambers (2011)
Solution of time-dependent PDE through component-wise approximation of matrix functionsIAENG Int. J. Appl. Math., 41
S Baroni, R Gebauer, OB Malcioğlu, Y Saad, P Umari, J Xian (2010)
Harnessing molecular excited states with Lanczos chainsJ. Phys-Condens. Mat., 22
Z Strakoš (2009)
Model reduction using the Vorobyev moment problemNumer. Algorithms, 51
S Güttel (2013)
Rational Krylov approximation of matrix functions: numerical methods and optimal pole selectionGAMM-Mitteilungen, 36
A Ruhe (1994)
Rational Krylov algorithms for nonsymmetric eigenvalue problemsIMA Vol. Math. Appl., 60
H Guo, RA Renaut (2004)
Estimation of uTf(a)v for large-scale unsymmetric matricesNumer. Linear Algebra Appl., 11
C Lanczos (1950)
An iteration method for the solution of the eigenvalue problem of linear differential and integral operatorsJ. Res. Nat. Bur. Stand., 45
V Druskin, L Knizhnerman (1998)
Extended Krylov subspaces: approximation of the matrix square root and related functionsSIAM J. Matrix Anal. Appl., 19
L Knizhnerman, V Simoncini (2010)
A new investigation of the extended Krylov subspace method for matrix function evaluationsNumer. Linear Algebra Appl., 17
I Moret, P Novati (2004)
RD-Rational approximations of the matrix exponential.BIT, 44
RW Freund, MH Gutknecht, NM Nachtigal (1993)
An implementation of the look-ahead Lanczos algorithm for non-Hermitian matricesSIAM J. Sci. Comput., 14
GH Golub, G Meurant (1994)
Numerical Analysis 1993, Pitman Research Notes in Mathematics Series, vol. 303
V Simoncini (2007)
A new iterative method for solving large-scale Lyapunov matrix equationsSIAM J. Sci. Comput., 29
TA Davis, Y Hu (2011)
The University of Florida Sparse Matrix CollectionACM T. Math. Software, 38
We present an extended Krylov subspace analogue of the two-sided Lanczos method, i.e., a method which, given a nonsingular matrix A and vectors b, c with b , c ≠ 0 $\left \langle {{\mathbf {b}},{\mathbf {c}}}\right \rangle \neq 0$ , constructs bi-orthonormal bases of the extended Krylov subspaces E m ( A , b ) ${\mathcal {E}}_{m}(A,{\mathbf {b}})$ and E m ( A T , c ) ${\mathcal {E}}_{m}(A^{T}\!,{\mathbf {c}})$ via short recurrences. We investigate the connection of the proposed method to rational moment matching for bilinear forms c T f(A)b, similar to known results connecting the two-sided Lanczos method to moment matching. Numerical experiments demonstrate the quality of the resulting approximations and the numerical behavior of the new extended Krylov subspace method.
Numerical Algorithms – Springer Journals
Published: Nov 28, 2016
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