Stability Analysis of QR factorization in an Oblique Inner Product
Stability Analysis of QR factorization in an Oblique Inner Product
复制标题
斜内积QR分解的稳定性分析
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
J. Langou
中科院分区：
文献类型：
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作者：
Bradley R. Lowery;J. Langou
本文考虑斜内积中QR分解的稳定性。斜内积由对称正定矩阵A定义，我们分析了两种算法，即基于A的因式分解和将问题转化为欧几里得情形。我们考虑的两种算法使用了Cholesky分解和特征值分解。分析了基于正态方程的Cholesky因子计算的算法。我们给出了数值实验，证明了误差界是紧的。最后，我们给出了这些算法以及Gram-Schmidt方法在并行结构上的性能结果。性能实验证明了通信避免算法的有效性。
In this paper we consider the stability of the QR factorization in an oblique inner product. The oblique inner product is defined by a symmetric positive definite matrix A. We analyze two algorithm that are based a factorization of A and converting the problem to the Euclidean case. The two algorithms we consider use the Cholesky decomposition and the eigenvalue decomposition. We also analyze algorithms that are based on computing the Cholesky factor of the normal equa- tion. We present numerical experiments to show the error bounds are tight. Finally we present performance results for these algorithms as well as Gram-Schmidt methods on parallel architecture. The performance experiments demonstrate the benefit of the communication avoiding algorithms.