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A Comparison of Limited-memory Krylov Methods for Stieltjes Functions of Hermitian Matrices

Given a limited amount of memory and a target accuracy, we propose and compare several polynomial Krylov methods for the approximation of $f(A){b}$, the action of a Stieltjes matrix function of a large Hermitian matrix on a vector. Using new error bounds and estimates, as well as existing results, we derive predictions of the practical performance of the methods and rank them accordingly. As byproducts, we derive new results on inexact Krylov iterations for matrix functions in order to allow for a fair comparison of rational Krylov methods with polynomial inner solves.


Read More: https://epubs.siam.org/doi/abs/10.1137/20M1351072

Ketersediaan

Informasi Detail

Judul Seri

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS; Vol.42 No.1 January-March 2021

No. Panggil

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Penerbit

: .,

Deskripsi Fisik

p. 83 - 107

Bahasa

English

ISBN/ISSN

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Klasifikasi

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Tipe Isi

-

Tipe Media

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Tipe Pembawa

-

Edisi

-

Subjek

MATRIX FUNCTION
KRYLOV METHOD
SHIFT-AND-INVERT METHOD
RESTARTED METHOD
STIELTJES FUNCTION
INEXACT KRYLOV METHOD
OUTER-INNER ITERATION

Info Detail Spesifik

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Pernyataan Tanggungjawab

Stefan Guttel, Marcel Schweitzer

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