METHOD OF GENERATING MATRIX FACTORS FOR A FINITE-DIMENSIONAL LINEAR TRANSFORM

摘要

A method of generating matrix factors for a finite-dimensional linear transform using a computer. The linear transform is represented by data values stored in a linear transformation matrix having a nonzero determinant. In one aspect, a first LU-decomposition is applied to the linear transformation matrix. Four matrices are generated from the LU-decomposition, including a first permutation matrix, a second permutation matrix, a lower triangular matrix having a unit diagonal, and a first upper triangular matrix. Additional elements include a third matrix Â, a signed permutation matrix Π such that A=ΠÂ, a permuted linear transformation matrix A′, a second upper triangular matrix U₁, wherein the second upper triangular matrix satisfies the relationship Â=U₁A′. The permuted linear transformation matrix is factored into a product including a lower triangular matrix L and an upper triangular matrix U. The linear transformation matrix is expressed as a product of the matrix factors.