Direct Secant Updates of Matrix Factorizations

DOI10.2307/2007282zbMath0482.65028OpenAlexW4254187022MaRDI QIDQ3940741

Earl S. Marwil, John E. jun. Dennis

Publication date: 1982

Full work available at URL: https://doi.org/10.2307/2007282

zbMATH Keywords

numerical resultsiterative methodsmatrix factorizationsNewton-like algorithmBroyden update methoddirect secant updates

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10)

Related Items

Multi-step quasi-Newton methods for optimization, Parallel and sequential Kaczmarz methods for solving underdetermined nonlinear equations, Solving systems of nonlinear equations by means of an accelerated successive orthogonal projections method, Two classes of multisecant methods for nonlinear acceleration, On the solution of highly structured nonlinear equations, Newton-like method with modification of the right-hand-side vector, The method of successive orthogonal projections for solving nonlinear simultaneous equations, An algorithm for solving sparse nonlinear least squares problems, A quasi-Newton method with sparse triple factorization for unconstrained minimization, Practical quasi-Newton methods for solving nonlinear systems, A quasi-Newton method with modification of one column per iteration, Solution of nonlinear systems of equations by an optimal projection method, Quasi-Newton methods with factorization scaling for solving sparse nonlinear systems of equations

Uses Software

• LINPACK
• minpack

Cites Work

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• Monitoring the stability of the triangular factorization of a sparse matrix
• Convergence Theorems for Least-Change Secant Update Methods
• Quasi-Newton Methods, Motivation and Theory
• An Estimate for the Condition Number of a Matrix
• A Characterization of Superlinear Convergence and Its Application to Quasi-Newton Methods
• Methods for Modifying Matrix Factorizations
• Modification of a Quasi-Newton Method for Nonlinear Equations with a Sparse Jacobian
• The Convergence of an Algorithm for Solving Sparse Nonlinear Systems
• Rank-one and Rank-two Corrections to Positive Definite Matrices Expressed in Product Form