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Proxy-GMRES : Preconditioning via GMRES in Polynomial Space

This paper proposes a class of polynomial preconditioners for solving non-Hermitian linear systems of equations. The polynomial is obtained from a least-squares approximation in polynomial space instead of a standard Krylov subspace. The process for building the polynomial relies on an Arnoldi-like procedure in a small dimensional polynomial space and is equivalent to performing GMRES in polynomial space. It is inexpensive and produces the desired polynomial in a numerically stable way. A few improvements to the basic scheme are discussed including the development of a short-term recurrence and the use of compound preconditioners. Numerical experiments, including a test with challenging nonnormal three-dimensional Helmholtz equations and a few publicly available sparse matrices, are provided to illustrate the performance of the proposed preconditioners.

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Informasi Detail

Judul Seri

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS; Vol.42 No.3 July-September 2021

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 1248-1267

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

HELMHOLTZ EQUATION
POLYNOMIAL PRECONDITIONING
POLYNOMIAL ITERATION
ORTHOGONAL POLYNOMIAL
SHORT-TERM RECURRENCE

Info Detail Spesifik

-

Pernyataan Tanggungjawab

Xin Ye, Yuanzhe Xi, Yousef Saad

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