An Augmented Lanczos Algorithm for the Efficient Computation of a Dot-Product of a Function of a Large Sparse Symmetric Matrix

机译：大型稀疏对称矩阵函数的乘积有效计算的增强Lanczos算法

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The Lanczos algorithm is appreciated in many situations due to its speed and economy of storage. However, the advantage that the Lanczos basis vectors need not be kept is lost when the algorithm is used to compute the action of a matrix function on a vector. Either the basis vectors need to be kept, or the Lanczos process needs to be applied twice. In this study we describe an augmented Lanczos algorithm to compute a dot product relative to a function of a large sparse symmetric matrix, without keeping the basis vectors.

机译：Lanczos算法由于其速度和存储经济性而在许多情况下受到赞赏。但是，当该算法用于计算矩阵函数对矢量的作用时，便失去了不需要保留Lanczos基矢量的优点。要么需要保留基向量，要么需要两次应用Lanczos过程。在这项研究中，我们描述了一种增强的Lanczos算法，以计算相对于大型稀疏对称矩阵的函数的点积，而无需保留基向量。

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《International Conference on Computational Science - ICCS 2003 Pt.3 Jun 2-4, 2003 Melbourne, Australia and St. Petersburg, Russia》|2003年|p.693-704|共12页
会议地点 Melbourne(AU) St. Petersburg(RU);Melbourne(AU) St. Petersburg(RU)
作者
Roger B. Sidje; Kevin Burrage; B. Philippe;
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Department of Mathematics University of Queensland Brisbane QLD 4072, Australia;

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原文格式 PDF
正文语种 eng
中图分类自动化技术、计算机技术;
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1. Four algorithms for the the efficient computation of truncated pivoted QR approximations to a sparse matrix [J] . G. W. Stewart Numerische Mathematik . 1999,第2期

机译：四种算法可以有效地计算稀疏矩阵的截断枢轴QR近似值
2. Efficient algorithm for sparse symmetric nonnegative matrix factorization [J] . Belachew Melisew Tefera Pattern recognition letters . 2019,第JULa期

机译：稀疏对称非负矩阵分解的高效算法
3. Efficient algorithm for sparse symmetric nonnegative matrix factorization [J] . Belachew Melisew Tefera Pattern recognition letters . 2019,第Jula期

机译：稀疏对称非负矩阵分解的高效算法
4. An Augmented Lanczos Algorithm for the Efficient Computation of a Dot-Product of a Function of a Large Sparse Symmetric Matrix [C] . Roger B. Sidje, Kevin Burrage, B. Philippe International conference on computational science . 2003

机译：一种增强的LanczoS算法，用于大稀疏对称矩阵的函数的高效计算
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机译：稀疏矩阵逆计算的快速算法。
6. Decoding the Encoding of Functional Brain Networks: an fMRI Classification Comparison of Non-negative Matrix Factorization (NMF) Independent Component Analysis (ICA) and Sparse Coding Algorithms [O] . Jianwen Xie, Pamela K. Douglas, Ying Nian Wu, -1

机译：解码功能性大脑网络的编码：非负矩阵分解（NMF）独立成分分析（ICA）和稀疏编码算法的fMRI分类比较
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机译：用于计算大稀疏对称矩阵特征值的频带Lanczos算法的实现方面
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机译：求解稀疏对称广义特征问题的移位块Lanczos算法

An Augmented Lanczos Algorithm for the Efficient Computation of a Dot-Product of a Function of a Large Sparse Symmetric Matrix

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