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Guaranteed Accuracy in Numerical Linear Algebra (Hardcover, 1993 ed.)
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Guaranteed Accuracy in Numerical Linear Algebra (Hardcover, 1993 ed.)
Series: Mathematics and Its Applications, 252
Expected to ship within 10 - 15 working days
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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 interest ing 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
solv ing 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 com lead putations is guaranteed. As far as the final
program product is con cerned, 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 abso lutely all errors of input data and machine
round-offs are taken into account. 2.
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