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A Fast Triangular Factorization Algorithm of the Inversion of Toeplitz Type Matrix

Meng Xu

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Abstract

According to triangular factorization of ″type″ matrix,a fast triangular factorization algorithm for the inversion of Toeplitz type matrix is presented. Firstly,let A be nonsingular,with the solution of linear equations,a recursive expression of A -1 is presented,a triangular factorization of A -1 is also given with the recursion. Secondly,with the theory given in the paper,the fast triangular factorization algorithm for the inversion of Toeplitz type matrix is presented. It is an O(mn 2) algorithm. Finally,numerical examples demonstrate the reliability.

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What this paper is about

According to triangular factorization of ″type″ matrix,a fast triangular factorization algorithm for the inversion of Toeplitz type matrix is presented. Firstly,let A be nonsingular,with the solution of linear equations,a recursive expression of A -1 is presented,a triangular factorization of A -1 is also given with the recursion. Secondly,with the theory given in the paper,the fast triangular factorization algorithm for the inversion of Toeplitz type matrix is presented. It is an O(mn 2) algorithm. Finally,numerical examples demonstrate the reliability.

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Available abstract

According to triangular factorization of ″type″ matrix,a fast triangular factorization algorithm for the inversion of Toeplitz type matrix is presented. Firstly,let A be nonsingular,with the solution of linear equations,a recursive expression of A -1 is presented,a triangular factorization of A -1 is also given with the recursion. Secondly,with the theory given in the paper,the fast triangular factorization algorithm for the inversion of Toeplitz type matrix is presented. It is an O(mn 2) algorithm. Finally,numerical examples demonstrate the reliability.

Key concepts: Toeplitz matrix, Invertible matrix, Incomplete LU factorization, Factorization, Triangular matrix, Incomplete Cholesky factorization, Dixon's factorization method, Mathematics

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