The geometric mean algorithm
TL;DR: The efiectiveness of the bisection algorithm is illustrated in the context of the computation of the eigenvalues of a symmetric tridiagonal matrix which has a very large condition number.
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About: This article is published in Applied Mathematics and Computation. The article was published on 01 Nov 2012. and is currently open access. The article focuses on the topics: Tridiagonal matrix & Geometric mean.
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Citations
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Efficient solvers for Armijo's backtracking problem
TL;DR: In this paper, the bisection algorithm for root-searching is transposed into a simple method that completes the same inexact line search in at most Ω(log_2 \log_{\beta} \epsilon/x_0 \rceil$ function evaluations.
Exploring the Spatial Relationship between Nighttime Light and Tourism Economy: Evidence from 31 Provinces in China
TL;DR: Based on NTL data and the basic tourism economy (TE) data from 31 provinces of China in 2019, this paper adopted a geographic concentration index, inconsistency index, spatial agglomeration coupling index, global and Local Moran's index and geographical detector to explore the spatial relationship between NTL and TE.
Efficient Solvers for Armijo's Backtracking Problem.
Ivo Fagundes David de Oliveira,Ricardo Hiroshi Caldeira Takahashi +1 more
TL;DR: This paper introduces efficient solvers for Armijo's backtracking problem, a widely used inexact line search procedure in optimization algorithms, with new methods requiring significantly fewer function evaluations, achieving time savings of 50-80% in numerical experiments.
References
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The Symmetric Eigenvalue Problem
Beresford N. Parlett
- 01 Jan 1980
TL;DR: Parlett as discussed by the authors presents mathematical knowledge that is needed in order to understand the art of computing eigenvalues of real symmetric matrices, either all of them or only a few.
3.7K
The Symmetric Eigenvalue Problem.
TL;DR: Parlett as discussed by the authors presents mathematical knowledge that is needed in order to understand the art of computing eigenvalues of real symmetric matrices, either all of them or only a few.
3.4K
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Lapack Users' Guide
Ed Anderson
- 01 Feb 1995
TL;DR: The third edition of LAPACK provided a guide to troubleshooting and installation of Routines, as well as providing examples of how to convert from LINPACK or EISPACK to BLAS.
3.2K
Numerical Methods for Large Eigenvalue Problems: Revised Edition
Yousef Saad
- 01 Jan 2011
TL;DR: Burden and Faires as mentioned in this paper gave an introduction to the theory and application of modern numerical approximation techniques for students taking a one or two-semester course in numerical analysis.
1.2K
A multiprocessor algorithm for the symmetric tridiagonal eigenvalue problem
Sy-Shin Lo,Berfnard Philippe,Ahmed H. Sameh +2 more
- 18 Nov 1985
TL;DR: Experiments on the Alliant FX/8 and CRAY X-MP/48 multiprocessors show that this algorithm achieves high speedup over BISECT and TINVIT; in fact it is much faster than TQL2 when all the eigenvalues and eigenvectors are required.
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