Matrix inverse operation method

Abstract

The invention relates to a matrix inverse operation method. The method comprises the steps of 1, conducting column pivoting LU decomposition, wherein a source matrix A is decomposed into a unit lower triangular matrix L, an upper triangular matrix U and a permutation matrix P according to the formula PA=LU; 2, conducting triangular matrix inversion, wherein the inverse matrix L-1 of the matrix L is obtained through matrix inversion, and matrix inversion is conducted on the transposed matrix of the matrix U and then transposition is conducted to obtain U-1; 3, finally conducting matrix multiplication, wherein the matrix U-1 and the matrix L-1 are multiplied, and column transformation is conducted on the matrix multiplication result according to the permutation matrix P to obtain a source matrix A-1. The method has the advantages that by using the column pivoting LU decomposition algorithm, the time complexity of the matrix inversion algorithm is effectively reduced, parallelizability of matrix inversion operation is improved, time for matrix inversion operation is shortened, matrix inversion operation of any order can be conducted, and the number of hardware resources can be increased or reduced according to count requirements of operation so that practical application requirements can be better met.

Description

technical field [0001] The invention relates to a matrix inversion method, in particular to a VLSI design method based on the matrix inversion operation of the time division multiplexing technology. Background technique [0002] There are many methods for matrix inversion, including adjoint matrix method, elementary transformation method, block matrix method, Gauss.Jordan elimination method, matrix decomposition method and so on. Among the various matrix inversion methods mentioned above, the adjoint matrix method requires a large number of determinants, and each determinant needs to calculate almost all matrix elements, which requires a large amount of calculation and requires a large storage space, which is not conducive to accomplish. [0003] Matrix decomposition is to decompose a matrix into the product of some simpler matrices, such as triangular matrix or unitary matrix, they all have certain characteristics, and it is easier to get the inverse matrix. Multiply the ...

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Problems solved by technology

[0011] If the decomposition does not carry out the selection of the pivot, it will affect the calculation accuracy and correctness, and even cause the calculation to fail when some singular matrices are encountered.

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