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.
展开▼
机译：一种使用计算机生成用于有限维线性变换的矩阵因子的方法。线性变换由存储在具有非零行列式的线性变换矩阵中的数据值表示。在一个方面，将第一LU分解应用于线性变换矩阵。从LU分解生成四个矩阵，包括第一置换矩阵，第二置换矩阵，具有单位对角线的下三角矩阵和第一上三角矩阵。附加元素包括第三矩阵Â，使A =Π的有符号置换矩阵,、置换线性变换矩阵A'，第二上三角矩阵U 1 ，其中第二上三角矩阵满足关系Â= U 1 A'。置换后的线性变换矩阵被分解为包括下三角矩阵L和上三角矩阵U的乘积。线性变换矩阵被表示为矩阵因子的乘积。
展开▼
