Newton's Iteration for Inversion of Cauchy-Like and Other Structured Matrices
نویسندگان
چکیده
منابع مشابه
Iterative inversion of structured matrices
Iterative processes for the inversion of structured matrices can be further improved by using a technique for compression and refinement via the least-squares computation. We review such processes and elaborate upon incorporation of this technique into the known frameworks.
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Newton’s iteration is a fundamental tool for numerical solutions of systems of equations. The well-known iteration ( ) 1 2 , 0 i i i X X I MX i + = − ≥ rapidly refines a crude initial approximation 0 X to the inverse of a general nonsingular matrix. In this paper, we will extend and apply this method to n n × structured matrices M , in which matrix multiplication has a lower computational cost....
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n this paper we present two fast numerical methods for computing the QR factorization of a Cauchy-like matrix C with data points lying on the real axis or on the unit circle in the complex plane. It is shown that the rows of the Q-factor of C give the eigenvectors of a rank structured matrix partially determined by some prescribed spectral data. This property establishes a basic connection betw...
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ژورنال
عنوان ژورنال: Journal of Complexity
سال: 1997
ISSN: 0885-064X
DOI: 10.1006/jcom.1997.0431