Two-step Gram-Schmidt downdating methods

Jesse Louis Barlow; Alicja Smoktunowicz; Hasan Erbay

doi:10.1117/12.448659

Two-step Gram-Schmidt downdating methods

Jesse Louis Barlow, Alicja Smoktunowicz, Hasan Erbay

Computer Science and Engineering

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

Abstract

Two-step Gram-Schmidt downdating methods were proposed for the the QR factorization. It showed that it is important that Gram-Schmidt procedures recover both the residual r and solution f. The vector f must be used in the downdating process to maintain good backward error in the new factorization. The new algorithms were proposed based on this observation.

Original language	English (US)
Pages (from-to)	273-284
Number of pages	12
Journal	Proceedings of SPIE - The International Society for Optical Engineering
Volume	4474
DOIs	https://doi.org/10.1117/12.448659
State	Published - 2001

All Science Journal Classification (ASJC) codes

Electronic, Optical and Magnetic Materials
Condensed Matter Physics
Computer Science Applications
Applied Mathematics
Electrical and Electronic Engineering

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10.1117/12.448659

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abstract = "Two-step Gram-Schmidt downdating methods were proposed for the the QR factorization. It showed that it is important that Gram-Schmidt procedures recover both the residual r and solution f. The vector f must be used in the downdating process to maintain good backward error in the new factorization. The new algorithms were proposed based on this observation.",

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AU - Erbay, Hasan

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AB - Two-step Gram-Schmidt downdating methods were proposed for the the QR factorization. It showed that it is important that Gram-Schmidt procedures recover both the residual r and solution f. The vector f must be used in the downdating process to maintain good backward error in the new factorization. The new algorithms were proposed based on this observation.

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AN - SCOPUS:0035763188

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JO - Proceedings of SPIE - The International Society for Optical Engineering

JF - Proceedings of SPIE - The International Society for Optical Engineering

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Two-step Gram-Schmidt downdating methods

Abstract

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