Details

Autor(en) / Beteiligte

• Godunov, S. K
• Antonov, A. G
• Kiriljuk, O. P
• Kostin, V. I

Titel

Guaranteed Accuracy in Numerical Linear Algebra [Elektronische Ressource]

Ist Teil von

• Mathematics and Its Applications : 252

Ort / Verlag

Dordrecht : Springer Netherlands

Erscheinungsjahr

1993

Link zu anderen Inhalten

• Volltext

Beschreibungen/Notizen

• There exists a vast literature on numerical methods of linear algebra. In our bibliography list, which is by far not complete, we included some monographs on the subject [46], [15], [32], [39], [11], [21]. The present book is devoted to the theory of algorithms for a single problem of linear algebra, namely, for the problem of solving systems of linear equations with non-full-rank matrix of coefficients. The solution of this problem splits into many steps, the detailed discussion of which are interesting problems on their own (bidiagonalization of matrices, computation of singular values and eigenvalues, procedures of deflation of singular values, etc. ). Moreover, the theory of algorithms for solutions of the symmetric eigenvalues problem is closely related to the theory of solving linear systems (Householder's algorithms of bidiagonalization and tridiagonalization, eigenvalues and singular values, etc. ). It should be stressed that in this book we discuss algorithms which to computer programs having the virtue that the accuracy of comlead putations is guaranteed. As far as the final program product is concerned, this means that the user always finds an unambiguous solution of his problem. This solution might be of two kinds: 1. Solution of the problem with an estimate of errors, where absolutely all errors of input data and machine round-offs are taken into account. 2