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Bunch, James R.

The weak and strong stability of algorithms in numerical linear algebra. (English) Zbl 0652.65032

Linear Algebra Appl. 88-89, 49-66 (1987).
The stability of algorithm in numeical linear algebra is discussed. The concept of stability is extended to notions of weak stability and strong stability. Justifications are given for these extensions, and the implications of error analysis in terms of these definitions are discussed. The concept of weak stability helps to clarify some of the controversy which has arisen concerning the stability of algorithms for Toeplitz systems.

Cited in 39 Documents

MSC:

65F35 Numerical computation of matrix norms, conditioning, scaling
15A12 Conditioning of matrices
65G50 Roundoff error

Keywords:

backward error analysis; conditioning; stability of algorithm; weak stability; strong stability; Toeplitz systems

Software:

LINPACK
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\textit{J. R. Bunch}, Linear Algebra Appl. 88--89, 49--66 (1987; Zbl 0652.65032)
Full Text: DOI

References:

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