Fast verification of solutions of matrix equations
Fast verification of solutions of matrix equations
复制标题
快速验证矩阵方程的解
DOI：
10.1007/s002110100310
复制
发表时间：
2002
影响因子：
2.1
通讯作者：
S. Rump
中科院分区：
文献类型：
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作者：
S. Oishi;S. Rump
摘要本文研究了一类矩阵方程
$ Ax = B $
其中A是
$n \times n$真实的矩阵，x和B是n-向量。假设一个近似解
$\tilde{x}$与近似LU分解一起给出。我们将提出快速算法来证明A的非奇异性和计算严格的误差界，
$\|A^{-1}B-\tilde{x}\|_{\infty}$。重点是边界的严格性。本文的目的是提出不同的算法，最快的与
验证步骤的计算成本为$\frac{2}{3} n^3$ flops，与LU分解相同。所提出的算法专门使用LU分解和所有其他矩阵和向量运算的库例程。
Summary. In this paper, we are concerned with a matrix equation
$ Ax = b $
where A is an
$n \times n$ real matrix and x and b are n-vectors. Assume that an approximate solution
$\tilde{x}$ is given together with an approximate LU decomposition. We will present fast algorithms for proving nonsingularity of A and for calculating rigorous error bounds for
$\|A^{-1}b-\tilde{x}\|_{\infty}$. The emphasis is on rigour of the bounds. The purpose of this paper is to propose different algorithms, the fastest with
$\frac{2}{3} n^3$ flops computational cost for the verification step, the same as for the LU decomposition. The presented algorithms exclusively use library routines for LU decomposition and for all other matrix and vector operations.
影响因子：
2.1
作者：
通讯作者：
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