Abstract
We study an iterative, locally quadratically convergent algorithm for solving Toeplitz systems of equations from [R. P. Brent, F. G. Gustavson and D. Y. Y. Yun. “Fast solution of Toeplitz systems of equations and computation of Padé approximations”,J. Algorithms, 1:259–295, 1980]. We introduce a new iterative algorithm that is locally quadratically convergent when used to solve symmetric positive definite Toeplitz systems. We present a set of numerical experiments on randomly generated symmetric positive definite Toeplitz matrices. In these experiments, our algorithm performed significantly better than the previously proposed algorithm.
Zusammenfassung
Wir studieren einen iterativen, lokal quadratisch konvergenten Algorithmus für die Lösung von Toeplitz-Systemen von Gleichungen von [R. P. Brent, F. G. Gustavson und D. Y. Y. Yun, “Fast solution of Toeplitz systems of equations and computation of Padé approximations”,J. Algorithms, 1:259–295, 1980]. Wir führen einen neuen iterativen Algorithmus ein, der lokal quadratisch konvergent ist, wenn er für positiv definite Toeplitz-Systeme gebraucht wird. Wir präsentieren eine Anzahl von numerischen Experimenten mit zufallsgenerierten, symmetrischen, positiv definiten Toeplitz-Matrizen. In diesen Experimenten ist unser Algorithmus entscheidend besser als der früher vorgeschlagene Algorithmus.
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Linzer, E., Vetterli, M. Iterative Toeplitz solvers with local quadratic convergence. Computing 49, 339–347 (1993). https://doi.org/10.1007/BF02248694
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DOI: https://doi.org/10.1007/BF02248694