# A two-sided short-recurrence extended Krylov subspace method for nonsymmetric matrices and its relation to rational moment matching

A two-sided short-recurrence extended Krylov subspace method for nonsymmetric matrices and its... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Numerical Algorithms Springer Journals

# A two-sided short-recurrence extended Krylov subspace method for nonsymmetric matrices and its relation to rational moment matching

, Volume 76 (1) – Nov 28, 2016
31 pages

/lp/springer_journal/a-two-sided-short-recurrence-extended-krylov-subspace-method-for-6MpkIVmo7A
Publisher
Springer US
Subject
Computer Science; Numeric Computing; Algorithms; Algebra; Theory of Computation; Numerical Analysis
ISSN
1017-1398
eISSN
1572-9265
D.O.I.
10.1007/s11075-016-0239-z
Publisher site
See Article on Publisher Site

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