Computation of Determinants, Adjoint Matrices, and Characteristic Polynomials without Division

被引：4

作者：

T. R. Seifullin

机构：

[1] National Academy of Sciences of Ukraine,Cybernetics Institute

来源：

Cybernetics and Systems Analysis | 2002年 / 38卷 / 5期

关键词：

computation of determinants; computation of adjoint matrices; computation of characteristic polynomials; computation without division; estimaton of computational algorithms; comparison of computational algorithms;

D O I：

10.1023/A:1021878507303

中图分类号：

学科分类号：

摘要：

Algorithms are proposed for computing the characteristic polynomial, determinant, and adjoint matrix for a n × n matrix and for solving a system of n-1 linear homogeneous equations in n variables by Cramer's rule using O(n4) ring operations (without the division operation) over an arbitrary commutative ring. The exponent in the estimate of the computation time can be additionally reduced if an algorithm of asymptotically fast matrix multiplication is used.

引用

页码：650 / 672

页数：22