Combinatorial Optimization Based on Conjugate Gradient and Orthogonal Triangular Decomposition for Sparse Recovery

2014 ◽  
Vol 11 (4) ◽  
pp. 1343-1356
Author(s):  
Hailing Xiong
Keyword(s):  
Combinatorial Optimization ◽  
Conjugate Gradient ◽  
Sparse Recovery ◽  
Triangular Decomposition

Sparse Recovery Using Conjugate Gradient and Orthogonal Triangular Decomposition

2013 ◽  
Vol 756-759 ◽  
pp. 2479-2483
Author(s):  
Xi Hua Peng ◽  
Shan Xiong Chen ◽  
Xiao Yan Liu
Keyword(s):  
Combinatorial Optimization ◽  
Conjugate Gradient ◽  
Matrix Factorization ◽  
Matching Pursuit ◽  
Optimal Solution ◽  
Sparse Recovery ◽  
Triangular Decomposition ◽  
Solution Sequence ◽  
Matching Pursuit Algorithm ◽  
Non Negative Matrix Factorization

In this article, we propose the matching pursuit algorithm of combinatorial optimization based CGLS and LSQR. We use non-negative matrix factorization for measuring discrepancy of solution sequence between CGLS and LSQR, and represent combinatorial optimization based CGLS and LSQ to choose optimal solution sequences. The experiments indicate our method is extended to the case where target signal has been corrupted by noise, it demonstrate perfectly recovery ability of signal with noise.

A new generalized shrinkage conjugate gradient method for sparse recovery

CALCOLO ◽  
2018 ◽  
Vol 56 (1) ◽  
Author(s):  
Hamid Esmaeili ◽  
Shima Shabani ◽  
Morteza Kimiaei
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Sparse Recovery

scholarly journals MPI+OpenMP parallel implementation of conjugate gradient method with preconditioner of block partial inverse triangular decomposition of IC2S and IC1

2021 ◽  
pp. 1-32
Author(s):  
Olga Yurievna Milyukova
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Parallel Implementation ◽  
Sparse Matrix ◽  
Triangular Decomposition ◽  
Algebraic Equations ◽  
First Order ◽  
Partial Inverse ◽  
Linear Algebraic Equations

The paper proposes a new preconditioner for solving systems of linear algebraic equations with a symmetric positively defined matrix by the method of conjugate gradients – Block Incomplete Inverse Cholesky BIIC preconditioner in combination with a triangular first-order decomposition "by value" - BIIC-IC1. The algorithm based on MPI+OpenMP techniques is proposed for the construction and application of the BIIC preconditioner combined with stabilized triangular decomposition of the second order "by value" (BIIC-IS2S). In this case, the BIIC-IC2S preconditioner uses the number of blocks multiple of the number of processors used and the number of threads used. Two algorithms based on MPI+OpenMP techniques are proposed for the construction and application of the BIIC-IC1 preconditioner. Comparative timing results for the MPI+OpenMP and MPI implementations of the proposed preconditioning used with the conjugate gradient method for a model problem and the sparse matrix collections SuiteSparse are presented.

Combinatorial Optimization Method Based on Evaluation of Proximate Optimality Using Correlation Coefficient

2015 ◽  
Vol 135 (4) ◽  
pp. 466-467 ◽  
Author(s):  
Masahide Morita ◽  
Hiroki Ochiai ◽  
Kenichi Tamura ◽  
Junichi Tsuchiya ◽  
Keiichiro Yasuda
Keyword(s):  
Combinatorial Optimization ◽  
Correlation Coefficient ◽  
Optimization Method
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