Solution of underdetermined nonlinear equations by stationary iteration methods

DOI10.1007/BF01395309zbMath0497.65026MaRDI QIDQ1170863

Klaus-Hermann Meyn

Publication date: 1983

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/132869

zbMATH Keywords

ill- conditioned problemsmethod of Kaczmarznonlinear image reconstruction in ultrasound tomographystationary iterationunderdetermined equations

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Numerical methods for integral transforms (65R10)

Related Items (14)

Parallel and sequential Kaczmarz methods for solving underdetermined nonlinear equations ⋮ Solving systems of nonlinear equations by means of an accelerated successive orthogonal projections method ⋮ General tracking control of arbitrary \(N\)-level quantum systems using piecewise time-independent potentials ⋮ Cooperative flow field estimation via relative and absolute motion-integration errors of multiple AUVs ⋮ Newton-like methods for solving underdetermined nonlinear equations with nondifferentiable terms ⋮ An accelerated successive orthogonal projections method for solving large-scale linear feasibility problems ⋮ On some optimization techniques in image reconstruction from projections ⋮ Levenberg-Marquardt revisited and parameter tuning of river regression models ⋮ A tree-based distributed method for cooperative flow field estimation ⋮ Presentation of a highly tuned multithreaded interval solver for underdetermined and well-determined nonlinear systems ⋮ Convergence rates for Kaczmarz-type regularization methods ⋮ Historical developments in convergence analysis for Newton's and Newton-like methods ⋮ Quasi-Newton methods for solving underdetermined nonlinear simultaneous equations ⋮ The projection method for solving nonlinear systems of equations under the most violated constraint control

Cites Work

• Block-iterative methods for consistent and inconsistent linear equations
• A composite Newton-Raphson gradient method for the solution of systems of equations
• An iterative procedure for the solution of constrained nonlinear equations with application to optimization problems
• Characterization of linear stationary iterative processes for solving a singular system of linear equations
• Projection method for solving a singular system of linear equations and its applications
• Über die Konvergenz der Iterationsverfahren zur Auflösung linearer Gleichungssysteme im Falle einer singulären Koeffizientenmatrix
• Extensions of Hildreth’s Row-Action Method for Quadratic Programming
• Row-Action Methods for Huge and Sparse Systems and Their Applications
• On the Solution of Singular and Semidefinite Linear Systems by Iteration
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