Modified Cholesky algorithms: A catalog with new approaches

DOI10.1007/s10107-007-0177-6zbMath1156.65023OpenAlexW2140918795MaRDI QIDQ948963

Dianne P. O'Leary, Haw-Ren Fang

Publication date: 16 October 2008

Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/1903/3674

zbMATH Keywords

algorithmnumerical examplesCholesky factorizationquasi-Newton methodspositive definite matrixsymmetric perturbationdescent directionmultivariate optimization

Mathematics Subject Classification ID

Programming involving graphs or networks (90C35) Numerical mathematical programming methods (65K05) Nonlinear programming (90C30) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items (8)

Euclidean distance matrix completion problems ⋮ Implementation of photon partial distinguishability in a quantum optical circuit simulation ⋮ Matrix Balancing Based Interior Point Methods for Point Set Matching Problems ⋮ MODIFIED CHOLESKY DECOMPOSITION FOR SOLVING THE MOMENT MATRIX IN THE RADIAL POINT INTERPOLATION METHOD ⋮ A filling function method for unconstrained global optimization ⋮ Using gradient directions to get global convergence of Newton-type methods ⋮ Flexible incomplete Cholesky factorization with multi‐parameters to control the number of nonzero elements in preconditioners ⋮ Exploiting Lower Precision Arithmetic in Solving Symmetric Positive Definite Linear Systems and Least Squares Problems

Cites Work

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• Some Stable Methods for Calculating Inertia and Solving Symmetric Linear Systems
• On the use of directions of negative curvature in a modified newton method
• A Modified Cholesky Algorithm Based on a Symmetric Indefinite Factorization
• Accurate Symmetric Indefinite Linear Equation Solvers
• Computing Modified Newton Directions Using a Partial Cholesky Factorization
• A Revised Modified Cholesky Factorization Algorithm
• On the reduction of a symmetric matrix to tridiagonal form

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