Numerical methods for the QCDd overlap operator. I. Sign-function and error bounds
Numerical methods for the QCDd overlap operator. I. Sign-function and error bounds
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DOI：
10.1016/s0010-4655(02)00455-1
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发表时间：
2002-02
影响因子：
6.3
通讯作者：
J. V. D. Eshof;Andreas Frommer;T. Lippert;K. Schilling;H. A. Vorst
中科院分区：
文献类型：
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作者：
J. V. D. Eshof;Andreas Frommer;T. Lippert;K. Schilling;H. A. Vorst
在格子量子色动力学中，重叠形式主义的数值和计算方面是非常苛刻的，因为矩阵向量乘积涉及厄米特威尔逊矩阵的符号函数。本文研究了几种计算矩阵符号函数与向量乘积的方法，特别是基于Lanczos的方法和部分分式展开法。我们的目标是双重的：我们给出了现实的比较已知的方法与新的方法，我们提出的误差范围，允许保证一个给定的精度时，终止的Lanczos方法和multishift-CG求解器，部分分数扩展方法内应用。
The numerical and computational aspects of the overlap formalism in lattice quantum chromodynamics are extremely demanding due to a matrix–vector product that involves the sign function of the Hermitian Wilson matrix. In this paper we investigate several methods to compute the product of the matrix sign-function with a vector, in particular Lanczos based methods and partial fraction expansion methods. Our goal is two-fold: we give realistic comparisons between known methods together with novel approaches and we present error bounds which allow to guarantee a given accuracy when terminating the Lanczos method and the multishift-CG solver, applied within the partial fraction expansion methods.