Please use this identifier to cite or link to this item: https://doi.org/10.15480/882.319
Title: Approximate inverses of almost singular matrices still contain useful information
Language: English
Authors: Rump, Siegfried M. 
Issue Date: 1990
Source: Technical report 90.1, Forschungsschwerpunkt Informations- und Kommunikationstechnik, TUHH, 1990
Abstract (english): It is well-known that, roughly spoken, a matrix inversion on a computer working in base B with t digits precision in the mantissa applied to a matrix of condition Bk produces approximately t-k correct digits of the inverse. For condition >> Bt one might conclude that an approximate inverse contains virtually useless information. In this note we will show that the latter is not true. An approximate inverse may still be useful, e.g. as a preconditioner. An extended set of examples show that preconditioning a matrix using an approximate inverse (computed in t digits precision) lowers the condition number by a factor Bt. As an example we develop an algorithm for solving systems of linear equations up to condition B2t strictly using t digits precision for all calculations and only allowing for double precision accumulation of inner products.
URI: http://tubdok.tub.tuhh.de/handle/11420/321
DOI: 10.15480/882.319
Institute: Zuverlässiges Rechnen E-19 
Type: Report (Bericht)
Appears in Collections:Publications (tub.dok)

Files in This Item:
File Description SizeFormat
Ru90b.pdf1,83 MBAdobe PDFThumbnail
View/Open
Show full item record

Page view(s)

408
Last Week
5
Last month
4
checked on May 22, 2019

Download(s)

213
checked on May 22, 2019

Google ScholarTM

Check

Export

Items in TORE are protected by copyright, with all rights reserved, unless otherwise indicated.