Recurrent neural networks for LU decomposition and Cholesky factorization

DOI10.1016/0895-7177(93)90121-EzbMath0804.90143OpenAlexW1968527606MaRDI QIDQ1324265

Jun Wang, Guang Wu

Publication date: 19 January 1995

Published in: Mathematical and Computer Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0895-7177(93)90121-e

zbMATH Keywords

Cholesky factorizationrecurrent neural networksLU decomposition

Mathematics Subject Classification ID

Sensitivity, stability, parametric optimization (90C31) Neural networks for/in biological studies, artificial life and related topics (92B20) Nonlinear systems in control theory (93C10) Mathematical programming (90C99)

Related Items (6)

A recurrent neural network for computing pseudoinverse matrices ⋮ Real-time computation of the eigenvectors of a class of positive definite matrices ⋮ Real-time computation of singular vectors ⋮ Recurrent neural networks for synthesizing linear control systems via pole placement ⋮ Properties and computation of continuous-time solutions to linear systems ⋮ Analog approach for the eigen-decomposition of positive definite matrices

Cites Work

• Massive memory buys little speed for complete, in-core sparse Cholesky factorizations on some scalar computers
• The accuracy of a parallel \(LU\) decomposition algorithm
• ``Neural computation of decisions in optimization problems
• A neural network for computing eigenvectors and eigenvalues
• Neural network approach to computing matrix inversion
• The average parallel complexity of Cholesky factorization
• Fast linear system solution by neural networks
• Recurrent neural networks for solving linear matrix equations
• Solving simultaneous linear equations using recurrent neural networks
• A recurrent neural network for real-time matrix inversion
• Dynamical systems that sort lists, diagonalize matrices, and solve linear programming problems
• Limiting Communication in Parallel Sparse Cholesky Factorization
• Neural networks for solving systems of linear equations and related problems
• Highly Parallel Sparse Cholesky Factorization
• Neural networks for solving systems of linear equations. II. Minimax and least absolute value problems
• Three-dimensional structured networks for matrix equation solving

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