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An Algorithm for the Inverse of a Class ofBlock Tridiagonal Matrices

Ruisheng Ran

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Abstract

The inverse of a class of block tridiagonal matrices is investigated. With the LU decomposition of the block tridiagonal matrix,an explicit expression of the block inverse elements is obtained. A relation between the inverse elements is found,and a new algorithm for inverting a block tridiagonal matrix is established. The computing complexity and computing time of this algorithm is lower than that of existed algorithms.

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What this paper is about

The inverse of a class of block tridiagonal matrices is investigated. With the LU decomposition of the block tridiagonal matrix,an explicit expression of the block inverse elements is obtained. A relation between the inverse elements is found,and a new algorithm for inverting a block tridiagonal matrix is established. The computing complexity and computing time of this algorithm is lower than that of existed algorithms.

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Available abstract

The inverse of a class of block tridiagonal matrices is investigated. With the LU decomposition of the block tridiagonal matrix,an explicit expression of the block inverse elements is obtained. A relation between the inverse elements is found,and a new algorithm for inverting a block tridiagonal matrix is established. The computing complexity and computing time of this algorithm is lower than that of existed algorithms.

Key concepts: Tridiagonal matrix, Tridiagonal matrix algorithm, Block (permutation group theory), Inverse, Mathematics, Algorithm, Matrix (chemical analysis), Block matrix

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