The simplest case of a linear equations problem is that of finding m unknowns by solving m linear algebraic non-homogeneous equations with given coefficients and constant terms. If this solution is carried out m times with the columns of the identity matrix as successive choices for the constant vec...

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Bibliographische Detailangaben

1. Verfasser:	Givens, Wallace (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Stanford, California 1959
Schriftenreihe:	Applied Mathematics and Statistics Laboratory <Stanford, Calif.>: Technical report 3
Schlagworte:	(Equations Algorithms Determinants(mathematics) Linear systems Mathematics Matrices(mathematics) Numerical analysis) Theoretical Mathematics Mathematik
Zusammenfassung:	The simplest case of a linear equations problem is that of finding m unknowns by solving m linear algebraic non-homogeneous equations with given coefficients and constant terms. If this solution is carried out m times with the columns of the identity matrix as successive choices for the constant vector, the resulting sets of solutions form the columns of the inverse of the matrix coefficients. Another situation which is disposed of very simply in a purely theoretical treatment but which is non-trivial in practice is that in which there are more equations than unknowns, yet a solution is known, or at least believed, to exist. The purpose of the present paper is to describe a method of solving in a routine way a class of linear algebraic problems which include the various special cases mentioned.