QR Factorization for The Regularized Least Squares Problem on Hypercubes

Jianping Zhu

doi:10.1016/0167-8191(93)90076-W

QR Factorization for The Regularized Least Squares Problem on Hypercubes

Jianping Zhu

Research output: Contribution to journal › Article › peer-review

Abstract

This paper discussed QR factorization algorithms for a special type of matrix arising from the application of the Tikhnov's regularization method to an ill-conditioned least squares problem. The matrix involved is half dense and half sparse. Householder transformation and the hybrid algorithm were implemented on iPSC/2 and iPSC/860 hypercubes. For a highly over-determined system, the row-oriented hybrid algorithm is faster than the column-oriented Householder transformation. The efficiency of the algorithms has been improved by overlapping communications with computations. BLAS routines are also used on iPSC/860 to enhance the performance of the algorithms.

Original language	American English
Journal	Parallel Computing
Volume	19
DOIs	https://doi.org/10.1016/0167-8191(93)90076-W
State	Published - Aug 1 1993

Keywords

QR factorization
Householder transformation
Intel hypercubes
Given's rotations
Hybrid algorithm
Timing results

Disciplines

Mathematics

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title = "QR Factorization for The Regularized Least Squares Problem on Hypercubes",

abstract = " This paper discussed QR factorization algorithms for a special type of matrix arising from the application of the Tikhnov's regularization method to an ill-conditioned least squares problem. The matrix involved is half dense and half sparse. Householder transformation and the hybrid algorithm were implemented on iPSC/2 and iPSC/860 hypercubes. For a highly over-determined system, the row-oriented hybrid algorithm is faster than the column-oriented Householder transformation. The efficiency of the algorithms has been improved by overlapping communications with computations. BLAS routines are also used on iPSC/860 to enhance the performance of the algorithms.",

keywords = "QR factorization, Householder transformation, Intel hypercubes, Given's rotations, Hybrid algorithm, Timing results",

author = "Jianping Zhu",

note = "Zhu, J. (1993). QR Factorization for The Regularized Least Squares Problem on Hypercubes. Parallel Computing, 19(8), 939-948, doi: 10.1016/0167-8191(93)90076-W.",

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PY - 1993/8/1

Y1 - 1993/8/1

N2 - This paper discussed QR factorization algorithms for a special type of matrix arising from the application of the Tikhnov's regularization method to an ill-conditioned least squares problem. The matrix involved is half dense and half sparse. Householder transformation and the hybrid algorithm were implemented on iPSC/2 and iPSC/860 hypercubes. For a highly over-determined system, the row-oriented hybrid algorithm is faster than the column-oriented Householder transformation. The efficiency of the algorithms has been improved by overlapping communications with computations. BLAS routines are also used on iPSC/860 to enhance the performance of the algorithms.

AB - This paper discussed QR factorization algorithms for a special type of matrix arising from the application of the Tikhnov's regularization method to an ill-conditioned least squares problem. The matrix involved is half dense and half sparse. Householder transformation and the hybrid algorithm were implemented on iPSC/2 and iPSC/860 hypercubes. For a highly over-determined system, the row-oriented hybrid algorithm is faster than the column-oriented Householder transformation. The efficiency of the algorithms has been improved by overlapping communications with computations. BLAS routines are also used on iPSC/860 to enhance the performance of the algorithms.

KW - QR factorization

KW - Householder transformation

KW - Intel hypercubes

KW - Given's rotations

KW - Hybrid algorithm

KW - Timing results

UR - https://engagedscholarship.csuohio.edu/scimath_facpub/71

UR - http://journals.ohiolink.edu/ejc/article.cgi?issn=01678191&issue=v19i0008&article=939_qfftrlspoh

U2 - 10.1016/0167-8191(93)90076-W

DO - 10.1016/0167-8191(93)90076-W

M3 - Article

VL - 19

JO - Parallel Computing

JF - Parallel Computing

ER -

QR Factorization for The Regularized Least Squares Problem on Hypercubes

Abstract

Keywords

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