ERROR ESTIMATES AND EVALUATION OF MATRIX FUNCTIONS VIA THE FABER TRANSFORM

Beckermann B; Reichel L

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ERROR ESTIMATES AND EVALUATION OF MATRIX FUNCTIONS VIA THE FABER TRANSFORM

机译：通过光纤变换估算矩阵函数的误差

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The need to evaluate expressions of the form f(A) or f(A)b, where f is a nonlinear function, A is a large sparse n x n matrix, and b is an n-vector, arises in many applications. This paper describes how the Faber transform applied to the field of values of Lambda can be used to determine improved error bounds for popular polynomial approximation methods based on the Arnoldi process. Applications of the Faber transform to rational approximation methods and, in particular, to the rational Arnoldi process also are discussed.

机译：在许多应用中都需要评估形式为f（A）或f（A）b的表达式，其中f是非线性函数，A是大的稀疏n x n矩阵，b是n向量。本文介绍了如何将应用到Lambda值字段的Faber变换用于确定基于Arnoldi过程的流行多项式逼近方法的改进误差范围。还讨论了Faber变换在有理逼近方法，尤其是有理Arnoldi过程中的应用。

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来源
《SIAM Journal on Numerical Analysis》 |2010年第5期|共35页
作者
Beckermann B; Reichel L;
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正文语种 eng
中图分类数值分析;
关键词
matrix function; polynomial approximation; rational approximation; Arnoldi process; rational Arnoldi process; error bound;

机译：矩阵函数;多项式逼近;有理逼近;Arnoldi过程;有理Arnoldi过程;误差界;

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1. ERROR ESTIMATES AND EVALUATION OF MATRIX FUNCTIONS VIA THE FABER TRANSFORM [J] . Beckermann B, Reichel L SIAM Journal on Numerical Analysis . 2010,第5期

机译：通过光纤变换估算矩阵函数的误差
2. Estimates for the error of approximation of classes of differentiable functions by Faber-Schauder partial sums [J] . Vakarchuk SB, Shchitov AN Sbornik. Mathematics . 2006,第3a4期

机译：用Faber-Schauder偏和估计可微函数类的近似误差
3. Minimum-error quantum distinguishability boundsfrom matrix monotone functions: A commenton "Two-sided estimates of minimum-errordistinguishability of mixed quantum statesvia generalized Holevo-Curlander bounds"[J. Math. Phys. 50, 032106 (2009)] [J] . Jon Tyson Journal of Mathematical Physics . 2009,第6期

机译：矩阵单调函数的最小误差量子可分辨性界：评“混合量子态的最小误差可辨性的两面估计”（广义霍夫-库兰德界）[J。数学。物理50，032106（2009）]
4. Faber Polynomial Coefficient Estimates For a Class of Analytic Bi-Univalent Functions [C] . Ala A. AMOURAH International Conference of Mathematics . 2019

机译：一类分析双单价函数的Faber多项式系数估计
5. Sensitivity of scattering function estimates to physical parameter measurement errors with applications to the wavelet transform domain estimator-correlator. [D] . Grove, Deborah Mary. 1998

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8. Estimating Tree Biomass Regressions and Their Error: Proceedings of the Workshop on Tree Biomass Regression Functions and Their Contribution to the Error of Forest Inventory Estimates Held at Syracuse, New York on May 26-30, 1986 [R] . Wharton, E. H. , Cunia, T. 1987

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ERROR ESTIMATES AND EVALUATION OF MATRIX FUNCTIONS VIA THE FABER TRANSFORM

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