IMPROVED RIGOROUS MULTIPLICATIVE PERTURBATION BOUNDS FOR THE GENERALIZED CHOLESKY FACTORIZATION AND THE CHOLESKY-LIKE FACTORIZATION

Farooq Aamir; Samar Mahvish; Li Hanyu; Mu Chunlai

首页> 外文期刊>Mathematical inequalities & applications >IMPROVED RIGOROUS MULTIPLICATIVE PERTURBATION BOUNDS FOR THE GENERALIZED CHOLESKY FACTORIZATION AND THE CHOLESKY-LIKE FACTORIZATION

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IMPROVED RIGOROUS MULTIPLICATIVE PERTURBATION BOUNDS FOR THE GENERALIZED CHOLESKY FACTORIZATION AND THE CHOLESKY-LIKE FACTORIZATION

机译：改进了广泛的尖端分解的严格乘法扰动界和尖弦状的因子

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摘要

Some improved rigorous multiplicative perturbation bounds for the generalized Cholesky factorization and the Cholesky-like factorization which are two generalizations of the classic Cholesky factorization are obtained by bringing together the modified matrix-vector equation approach with the method of Lyapunov majorant function and the Banach fixed point theorem. These bounds are continually tighter than the corresponding ones given in the literature.

机译：通过将改进的矩阵 - 矢量方程方法与Lyapunov Maddent函数的方法和Banach传动点的方法一起实现了一种改进的锥形分解和具有经典尖端分解的两个概括的尖端的乘法分解和具有经典凿形分解的巧克力形状的尖峰状分解。定理。这些界限比文献中给出的相应的界限不断更严格。

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来源
《Mathematical inequalities & applications》 |2019年第1期|共17页
作者
Farooq Aamir; Samar Mahvish; Li Hanyu; Mu Chunlai;
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作者单位

Chongqing Univ Coll Math &

Stat Chongqing 401331 Peoples R China;

Chongqing Univ Coll Math &

Stat Chongqing 401331 Peoples R China;

Chongqing Univ Coll Math &

Stat Chongqing 401331 Peoples R China;

Chongqing Univ Coll Math &

Stat Chongqing 401331 Peoples R China;

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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
Generalized Cholesky factorization; Cholesky-like factorization; multiplicative perturbation; Lyapunov majorant fuction; Banach fixed point theorem; rigorous perturbation bound;

机译：广义凿次的分解;尖峰状形式;乘法扰动;Lyapunov主要职业;Banach Teact Point定理;严格的扰动约束;

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专利

1. IMPROVED RIGOROUS MULTIPLICATIVE PERTURBATION BOUNDS FOR THE GENERALIZED CHOLESKY FACTORIZATION AND THE CHOLESKY-LIKE FACTORIZATION [J] . Farooq Aamir, Samar Mahvish, Li Hanyu, Mathematical inequalities & applications . 2019,第1期

机译：改进了广泛的尖端分解的严格乘法扰动界和尖弦状的因子
2. New rigorous perturbation bounds for the Cholesky-like factorization of skew-symmetric matrix [J] . Li Hanyu, Wei Yimin, Yang Yanfei Linear Algebra and its Applications . 2016,第Null期

机译：偏对称矩阵的Cholesky分解的新严格扰动界
3. New rigorous perturbation bounds for the generalized Cholesky factorization [J] . Li Hanyu, Yang Yanfei Applied mathematics and computation . 2015,第Null期

机译：广义Cholesky分解的新严格摄动界。
4. Perturbation Analyses for the Cholesky Factorization with Backward Rounding Errors [C] . Xiao-Wen Chang 6th Workshop on Scientific Computing 10-12 March, 1997 Hong Kong . 1997

机译：具有倒圆误差的Cholesky因式分解的摄动分析
5. Matrix factorizations, triadic matrices, and modified Cholesky factorizations for optimization [D] . Fang, Haw-ren 2006

机译：矩阵分解，三元矩阵和改进的Cholesky分解以进行优化
6. A unified framework for sparse non-negative least squares using multiplicative updates and the non-negative matrix factorization problem [O] . Igor Fedorov, Alican Nalci, Ritwik Giri, -1

机译：使用乘法更新和非负矩阵分解问题的稀疏非负最小二乘的统一框架
7. Improved rigorous multiplicative perturbation bounds for the generalized Cholesky factorization and the Cholesky-like factorization [O] . Aamir Farooq, Mahvish Samar, Hanyu Li, 2019

机译：改进的常规尖端分解和尖弦状分解的严格乘法扰动界限
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

IMPROVED RIGOROUS MULTIPLICATIVE PERTURBATION BOUNDS FOR THE GENERALIZED CHOLESKY FACTORIZATION AND THE CHOLESKY-LIKE FACTORIZATION

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