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Inversion formulas and linear complexity algorithm for diagonal plus semiseparable matrices. (English) Zbl 0870.65020

Sums of diagonal and semiseparable matrices belong to the class of structured matrices which arises in numerical applications. Fast \(O(N)\) algorithms for their inversion were developed earlier under additional restrictions which were a source of instability. For semiseparable matrices of order one these restrictions are eliminated.

MSC:

65F05 Direct numerical methods for linear systems and matrix inversion
Full Text: DOI

References:

[1] Gohberg, I.; Kailath, T.; Koltracht, I., Linear complexity algorithms for semiseparable matrices, Integral Equations and Operator Theory, 8, 780-804 (1985) · Zbl 0592.65015
[2] Gohberg, I.; Kailath, T.; Koltracht, I., A note on diagonal innovation matrices, Acoustics, Speech and Signal Processing, 7, 1068-1069 (1987)
[3] Gohberg, I.; Kaashoek, M. A., Time varying linear systems with boundary conditions and integral operators, 1. The transfer operator and its properties, Integral Equations and Operator Theory, 7, 325-391 (1984) · Zbl 0541.93049
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