Stability Analysis of QR factorization in an Oblique Inner Product
arXiv:1401.5171
Abstract
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.
20 pages
Cited by in corpus (3)
- hIPPYlib: An Extensible Software Framework for Large-Scale Inverse Problems Governed by PDEs; Part I: Deterministic Inversion and Linearized Bayesian Inference
- Shifted CholeskyQR for computing the QR factorization of ill-conditioned matrices
- Efficient implementations of the modified Gram-Schmidt orthogonalization with a non-standard inner product