A Note on Inexact Inner Products in GMRES | PERPUSTAKAAN UNIVERSITAS KATOLIK PARAHYANGAN

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A Note on Inexact Inner Products in GMRES

Gratton, Serge - Nama Orang; Toint, Philippe L. - Nama Orang; Titley-Peloquin, David - Nama Orang; Simon, Ehouarn - Nama Orang;

We show to what extent the accuracy of the inner products computed in the GMRES iterative solver can be reduced as the iterations proceed without affecting the convergence rate or final accuracy achieved by the iterates. We bound the loss of orthogonality in GMRES with inexact inner products. We use this result to bound the ratio of the residual norm in inexact GMRES to the residual norm in exact GMRES and give a condition under which this ratio remains close to 1. We illustrate our results with examples in variable floating-point arithmetic.

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Informasi Detail

Judul Seri: SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS; Vol.43 No.3 July-September 2022
No. Panggil: -
Penerbit: : .,
Deskripsi Fisik: p. 1406-1422
Bahasa: English
ISBN/ISSN: -
Klasifikasi: NONE
Tipe Isi: -
Tipe Media: -
Tipe Pembawa: -
Edisi: -
Subjek: ARNOLDI ALGORITHM
GMRES ALGORITHM
INEXACT INNER PRODUCTS
VARIABLE PRECISION ARITHMETIC
Info Detail Spesifik: https://doi.org/10.1137/20M1320018
Pernyataan Tanggungjawab: Serge Gratton, Ehouarn Simon, David Titley-Peloquin, Philippe L. Toint

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