QR factorization revisited.

机译：再谈QR因式分解。

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A general framework capturing known QR factorization methods is presented. A relationship between the major classes of methods leads to a new, efficient and accurate method for computing the Cholesky decomposition of ( I − qqT). Incorporating the new Cholesky decomposition into an accurate QR factorization algorithm is expressed as a splitting of orthogonal Hessenberg matrices. Computation is further optimized by introducing a new factorization for orthogonal Hessenberg matrices called DST factorization. A QR algorithm based on DST factorization is presented that has accuracy comparable to Householder transformations, the flexibility of Givens rotations and the lowest operation count of known methods. Also, it has provable bounds on the computation. Results from computing the QR factorization of several ill-conditioned and rank deficient matrices are presented.

机译：提出了捕获已知QR因式分解方法的通用框架。主要方法之间的关系导致了一种新的，高效且准确的计算（ T ）的Cholesky分解的方法。将新的Cholesky分解合并到精确的QR分解算法中表示为正交Hessenberg矩阵的分裂。通过为正交Hessenberg矩阵引入一种称为DST因式分解的新因式分解来进一步优化计算。提出了一种基于DST分解的QR算法，其精度可与Householder变换相媲美，Givens旋转的灵活性以及已知方法的最低运算量。而且，它在计算上有可证明的界限。给出了计算几种病态和秩不足矩阵的QR因式分解的结果。

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作者
Barszcz, Eric.;
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作者单位

University of California, Santa Cruz.;

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授予单位 University of California, Santa Cruz.;
学科 Computer Science.; Engineering General.; Mathematics.
学位 Ph.D.
年度 2002
页码 115 p.
总页数 115
原文格式 PDF
正文语种 eng
中图分类自动化技术、计算机技术;工程基础科学;数学;
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专利

1. SHIFTED CHOLESKY QR FOR COMPUTING THE QR FACTORIZATION OF ILL-CONDITIONED MATRICES [J] . Fukaya Takeshi, Kannan Ramaseshan, Nakatsukasa Yuji, SIAM Journal on Scientific Computing . 2020,第1期

机译：转移Cholesky QR计算不良矩阵的QR分解
2. Computing {2,4} and {2,3}-inverses Using SVD-like Factorizations and QR Factorization [J] . Bilall I. Shaini Filomat . 2016,第2期

机译：使用类SVD分解和QR分解计算{2,4}和{2,3}逆
3. ACCURATE MATRIX FACTORIZATION: INVERSE LU AND INVERSE QR FACTORIZATIONS [J] . Ogita T SIAM Journal on Matrix Analysis and Applications . 2010,第5期

机译：精确矩阵分解：LU逆和QR逆
4. A New QR Factorization Method by Recursive Blocked Gram-Schmidt Algorithm and Recursive Blocked Cholesky Factorization [C] . Shinya Ozawa, Yohsuke Hosoda, Takemitsu Hasegawa International Conference on Numerical Analysis and Applied Mathematics . 2015

机译：递归阻塞克施密特算法和递归阻塞Cholesky系数的新QR分解方法
5. Maintaining high performance in the QR factorization while scaling both problem size and parallelism. [D] . Samuel, Siju. 2011

机译：在QR分解中保持高性能，同时扩展问题大小和并行度。
6. Evolutionary profiles from the QR factorization of multiple sequence alignments [O] . Anurag Sethi, Patrick ODonoghue, Zaida Luthey-Schulten 2005

机译：来自多个序列比对的QR分解的进化谱
7. Hyperbolic QR factorization for J-spectral factorization of polynomial matrices [O] . Didier Henrion 2004

机译：多项式矩阵J谱分解的双曲QR分解
8. Cholesky Factorization, Schur Complements, Correlation Coefficients, Angles between Vectors, and the QR Factorization [R] . Delosme, J.-M., Ipsen, I. C., Paige, C. C. 1988

机译：Cholesky分解，schur补，相关系数，矢量之间的角度和QR分解

QR factorization revisited.

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