Updating the QR factorization and the least squares problem
Updating the QR factorization and the least squares problem
复制标题
DOI：
--
复制
发表时间：
2008-11
期刊：
影响因子：
--
通讯作者：
S. Hammarling;C. Lucas
中科院分区：
文献类型：
--
作者：
S. Hammarling;C. Lucas
在本文中，我们处理的问题更新QR分解，应用到最小二乘问题。给出了计算因子分解A1 = Q1 R1的算法，其中A1是矩阵A = QR，在它增加或删除了一些行或列之后。这是通过更新因子Q和R来实现的，我们证明了这比从头开始计算A1的因子分解要快得多。我们考虑的算法，利用3级BLAS在可能的情况下，不限制的尺寸A或增加或删除的行数和列数。对于我们的一些算法，我们提出了Fortran 77 LAPACK风格的代码，并显示我们的更新因子的向后误差与A1的QR分解的误差界相当。
In this paper we treat the problem of updating the QR factorization, with applications to the least squares problem. Algorithms are presented that compute the factorization A1 = Q1 R1, where A1 is the matrix A = QR after it has had a number of rows or columns added or deleted. This is achieved by updating the factors Q and R, and we show this can be much faster than computing the factorization of A1 from scratch. We consider algorithms that exploit the Level 3 BLAS where possible and place no restriction on the dimensions of A or the number of rows and columns added or deleted. For some of our algorithms we present Fortran 77 LAPACK-style code and show the backward error of our updated factors is comparable to the error bounds of the QR factorization of A1.