Accelerated Residual Methods for the Iterative Solution of Systems of Equations

We present accelerated residual methods for the iterative solution of systems of equations by leveraging recent developments in accelerated gradient methods for convex optimization. The stability p...

[1]  R. Fletcher,et al.  A New Approach to Variable Metric Algorithms , 1970, Comput. J..

[2]  Yurii Nesterov,et al.  Introductory Lectures on Convex Optimization - A Basic Course , 2014, Applied Optimization.

[3]  William L. Briggs,et al.  A multigrid tutorial , 1987 .

[4]  D. Young.  Iterative methods for solving partial difference equations of elliptic type , 1954 .

[5]  M. Saunders,et al.  Solution of Sparse Indefinite Systems of Linear Equations , 1975 .

[6]  Wolfgang Hackbusch,et al.  Multi-grid methods and applications , 1985, Springer series in computational mathematics.

[7]  Hedy Attouch,et al.  The Rate of Convergence of Nesterov's Accelerated Forward-Backward Method is Actually Faster Than 1/k2 , 2015, SIAM J. Optim..

[8]  T. Chan,et al.  Nonlinearly Preconditioned Krylov Subspace Methods for Discrete Newton Algorithms , 1984 .

[9]  D. Mavriplis.  Multigrid Strategies for Viscous Flow Solvers on Anisotropic Unstructured Meshes , 1997 .

[10]  D. Goldfarb.  A family of variable-metric methods derived by variational means , 1970 .

[11]  D. Brandt,et al.  Multi-level adaptive solutions to boundary-value problems math comptr , 1977 .

[12]  D. Keyes,et al.  Jacobian-free Newton-Krylov methods: a survey of approaches and applications , 2004 .

[13]  Henk A. van der Vorst,et al.  Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems , 1992, SIAM J. Sci. Comput..

[14]  John Darzentas,et al.  Problem Complexity and Method Efficiency in Optimization , 1983 .

[15]  Yurii Nesterov,et al.  Smooth minimization of non-smooth functions , 2005, Math. Program..

[16]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[17]  Y. Nesterov.  A method for solving the convex programming problem with convergence rate O(1/k^2) , 1983 .

[18]  R. Freund,et al.  QMR: a quasi-minimal residual method for non-Hermitian linear systems , 1991 .

[19]  C. G. Broyden.  The Convergence of a Class of Double-rank Minimization Algorithms 1. General Considerations , 1970 .

[20]  Yousef Saad,et al.  Hybrid Krylov Methods for Nonlinear Systems of Equations , 1990, SIAM J. Sci. Comput..

[21]  D. Shanno.  Conditioning of Quasi-Newton Methods for Function Minimization , 1970 .

[22]  M. Hestenes,et al.  Methods of conjugate gradients for solving linear systems , 1952 .

[23]  Yurii Nesterov,et al.  Gradient methods for minimizing composite functions , 2012, Mathematical Programming.