article Free Access Share on The Approximate Solution of Matrix Problems Author: A. S. Householder Oak Ridge National Laboratory, Oak Ridge, Tennessee Oak Ridge National Laboratory, Oak Ridge, TennesseeView Profile Authors Info & Claims Journal of the ACMVolume 5Issue 3pp 205–243https://doi.org/10.1145/320932.320933Published:01 July 1958Publication History 56citation839DownloadsMetricsTotal Citations56Total Downloads839Last 12 Months57Last 6 weeks6 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

The tridiagonalization of a symmetric matrix by a sequence of plane rotations constitutes the first of the two major steps in the computation of the proper values by one of the methods now in common use.This method was first programmed by J. W. Givens (1954) for the ORACLE, and his description includes a detailed analysis of the errors generated in the computation.The analysis of the errors in the tridiagonalization, however, is extremely laborious.It is the purpose of the present note to outline an approach which, though yielding less sharp bounds, seems to be considerably simpler, and possibly capable of extension to other routines.The actual computation of the proper values themselves is carried out by an essentially independent routine, and the errors generated in this phase of the computation will not be considered here.Before the analysis can be presented it is necessary to review the nature of the computation.The first step is to rotate in the (2,3)-coordinate plane so that if A = A T = (ol~3) is the original matrix, and A' = (a'~j) the rotated matrix, * Presented at the meeting of the Association, June 11-13, 1958.

article Free Access Share on Unitary Triangularization of a Nonsymmetric Matrix Author: Alston S. Householder Oak Ridge National Laboratory, Oak Ridge, Tennessee Oak Ridge National Laboratory, Oak Ridge, TennesseeView Profile Authors Info & Claims Journal of the ACMVolume 5Issue 4Oct. 1958 pp 339–342https://doi.org/10.1145/320941.320947Published:01 October 1958Publication History 378citation2,789DownloadsMetricsTotal Citations378Total Downloads2,789Last 12 Months212Last 6 weeks33 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

article Free AccessRetiring Presidential Address Author: A. S. Householder Oak Ridge National Laboratory, Oak Ridge, Tenn. Oak Ridge National Laboratory, Oak Ridge, Tenn.View Profile Authors Info & Claims Journal of the ACMVolume 4Issue 1Jan. 1957 pp 1–4https://doi.org/10.1145/320856.320857Published:01 January 1957Publication History 1citation390DownloadsMetricsTotal Citations1Total Downloads390Last 12 Months10Last 6 weeks2 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

1. Introduction.This paper discusses the numerical solution of certain matrix problems which are inverses of the familiar characteristic value problem.

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article Free AccessBibliography on Numerical Analysis Author: Alston S. Householder Oak Ridge National Laboratory, Oak Ridge, Tenn Oak Ridge National Laboratory, Oak Ridge, TennView Profile Authors Info & Claims Journal of the ACMVolume 3Issue 2April 1956 pp 85–100https://doi.org/10.1145/320825.320829Published:01 April 1956Publication History 5citation721DownloadsMetricsTotal Citations5Total Downloads721Last 12 Months21Last 6 weeks1 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

article Free Access Share on On the Convergence of Matrix Iterations Author: Alston S. Householder Oak Ridge National Laboratory, Oak Ridge, Tenn. Oak Ridge National Laboratory, Oak Ridge, Tenn.View Profile Authors Info & Claims Journal of the ACMVolume 3Issue 4pp 314–324https://doi.org/10.1145/320843.320851Published:01 October 1956Publication History 19citation875DownloadsMetricsTotal Citations19Total Downloads875Last 12 Months93Last 6 weeks17 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF