实线性代数方程组的统一算法与类型判别

A Universal Algorithm for Solving Real Linear Algebraic Equations and Distinguishing Its Type

对实线性代数方程组AX=F,用A=(a_(ij))_(m×n)的奇异值分解和Moore-Penrose广义逆理论,对无论m大于、等于或小于n、方程组相容与否、良态还是病态,给出统一求解公式和类型判别。应用该法在微机上计算了例题。

Basing on the theory for the singular values decomposition of matrix A = (aij)m×n and its Moor-Penrose generalized inverse matrix, a universal solution formula of real linear algebraic equations AX = F, whether which is consistent or not, well conditioned or not, is given, the way to determine the equations' type is found. As one application of this algorithm, the equations in the paper are solved with microcomputer.