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A Block Bidiagonalization Method for Fixed-Accuracy Low-Rank Matrix Approximation

We present randUBV, a randomized algorithm for matrix sketching based on the block Lanzcos bidiagonalization process. Given a matrix A
, it produces a low-rank approximation of the form UBVT, where U and V have orthonormal columns in exact arithmetic and B is block bidiagonal. In finite precision, the columns of both U and V will be close to orthonormal. Our algorithm is closely related to the randQB algorithms of Yu, Gu, and Li [SIAM J. Matrix Anal. Appl., 39 (2018), pp. 1339--1359]. in that the entries of B are incrementally generated and the Frobenius norm approximation error may be efficiently estimated. It is therefore suitable for the fixed-accuracy problem and so is designed to terminate as soon as a user input error tolerance is reached. Numerical experiments suggest that the block Lanczos method is generally competitive with or superior to algorithms that use power iteration, even when A has significant clusters of singular values.

Ketersediaan

Informasi Detail

Judul Seri

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS; Vol.43 No.2 April-June 2022

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 661-680

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

RANDOMIZED ALGORITHM
LOW-RANK MATRIX APPROXIMATION
BLOCK LANCZOS
FIXED-ACCURACY PROBLEM

Info Detail Spesifik

https://doi.org/10.1137/21M1397866

Pernyataan Tanggungjawab

Eric Hallman

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