The implementation of a generalized cross validation algorithm using deflation techniques for linear systems

DOI10.1016/0168-9274(95)00016-NzbMath0853.65043OpenAlexW2087526871MaRDI QIDQ1917400

A. Williams, Kevin Burrage, Jocelyne Erhel, Bert Pohl

Publication date: 5 January 1997

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0168-9274(95)00016-n

zbMATH Keywords

comparisonlinear systemsparallel computationJacobi iterationLU factorizationgeneralized cross validation function minimizationparallel smoothingreverse Gauss-Seidel deflation

Mathematics Subject Classification ID

Numerical smoothing, curve fitting (65D10) Iterative numerical methods for linear systems (65F10) Parallel numerical computation (65Y05)

Related Items

Fast generalized cross validation using Krylov subspace methods ⋮ GCV for Tikhonov regularization via global Golub–Kahan decomposition ⋮ Maximizing the predictivity of smooth deformable image warps through cross-validation

Cites Work

• Communication complexity of the Gaussian elimination algorithm on multiprocessors
• Solving banded systems on a parallel processor
• Analyzing stationary and periodic solutions of systems of parabolic partial differential equations by using singular subspaces as reduced basis
• Restarted GMRES preconditioned by deflation
• Parallel Sparse LU Decomposition on a Mesh Network of Transputers
• Stabilization of Unstable Procedures: The Recursive Projection Method
• A Stochastic Estimator of the Trace of the Influence Matrix for Laplacian Smoothing Splines
• The Computation of Generalized Cross-Validation Functions Through Householder Tridiagonalization with Applications to the Fitting of Interaction Spline Models
• A Deflation Technique for Linear Systems of Equations
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