On the numerical solution of ill‐conditioned linear systems by regularization and iteration

Summary We propose to reduce the (spectral) condition number of a given linear system by adding a suitable diagonal matrix to the system matrix, in particular by shifting its spectrum. Iterative procedures are then adopted to recover the solution of the original system. The case of real symmetric po...

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Veröffentlicht in:Numerical linear algebra with applications 2021-01, Vol.28 (1), p.n/a
1. Verfasser: Spigler, Renato
Format: Artikel
Sprache:eng
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Zusammenfassung:Summary We propose to reduce the (spectral) condition number of a given linear system by adding a suitable diagonal matrix to the system matrix, in particular by shifting its spectrum. Iterative procedures are then adopted to recover the solution of the original system. The case of real symmetric positive definite matrices is considered in particular, and several numerical examples are given. This approach has some close relations with Riley's method and with Tikhonov regularization. Moreover, we identify approximately the aforementioned procedure with a true action of preconditioning.
ISSN:1070-5325
1099-1506
DOI:10.1002/nla.2335