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Computing the Square Root of a Low-Rank Perturbation of the Scaled Identity Matrix

We consider the problem of computing the square root of a perturbation of the scaled identity matrix,
, where and are matrices with . This problem arises in various applications, including computer vision and optimization methods for machine learning. We derive a new formula for the th root of that involves a weighted sum of powers of the th root of the matrix . This formula is particularly attractive for the square root, since the sum has just one term when . We also derive a new class of Newton iterations for computing the square root that exploit the low-rank structure. We test these new methods on random matrices and on positive definite matrices arising in applications. Numerical experiments show that the new approaches can yield a much smaller residual than existing alternatives and can be significantly faster when the perturbation has low rank.

Ketersediaan

Informasi Detail

Judul Seri

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS; Vol.44 No.1 January-March 2023

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 156-174

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

MATLAB
NEWTON ITERATION
MATRIX SQUARE ROOT
MATRIX ITERATION
LOW-RANK UPDATE
MATRIX PTH ROOT

Info Detail Spesifik

https://doi.org/10.1137/22M1471559

Pernyataan Tanggungjawab

Massimiliano Fasi, Nicholas J. Higham, Xiaobo Liu

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