Accuracy of one step of the Falk-Langemeyer method

We present a new subtle technique in accuracy analysis which we use to prove the accuracy of the Falk-Langemeyer method for solving a real definite generalized eigenvalue problem A x = λ B x . We derive the exact expressions for the errors caused by finite arithmetic computation in one step of the m...

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Bibliographic Details
Published in:Numerical algorithms 2015-04, Vol.68 (4), p.645-670
Main Author: Matejas, Josip
Format: Article
Language:English
Subjects:
Accuracy
Algebra
Algorithms
Arithmetic
Computation
Computer Science
Eigenvalues
Errors
Mathematical analysis
Mathematical models
Matrices (mathematics)
Numeric Computing
Numerical Analysis
Original Paper
Theory of Computation
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Summary:We present a new subtle technique in accuracy analysis which we use to prove the accuracy of the Falk-Langemeyer method for solving a real definite generalized eigenvalue problem A x = λ B x . We derive the exact expressions for the errors caused by finite arithmetic computation in one step of the method. We consider separately the case of diagonal, positive definite matrix B
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-014-9865-5