2013, 1st ed., Numerical mathematics and scientific computation, ISBN 9780199655410, Volume 9780199655410, xv, 391

This book offers a detailed treatment of the mathematical theory of Krylov subspace methods with focus on solving systems of linear algebraic equations....

Sparse matrices | applied mathematics | Mathematical optimization | Conjugate gradient method | Cost of computations | Problem of moments | Krylov subspace methods | GMRES | Orthogonal polynomials | Projection methods | Jacobi matrices | Cyclic invariant subspaces | Short recurrences | Continued fractions | Convergence analysis | Iterative methods (Mathematics)

Sparse matrices | applied mathematics | Mathematical optimization | Conjugate gradient method | Cost of computations | Problem of moments | Krylov subspace methods | GMRES | Orthogonal polynomials | Projection methods | Jacobi matrices | Cyclic invariant subspaces | Short recurrences | Continued fractions | Convergence analysis | Iterative methods (Mathematics)

Book

1974, Lecture notes in mathematics, ISBN 0387068058, Volume 394., 183

Book

Mathematical Programming, ISSN 0025-5610, 2/2013, Volume 137, Issue 1, pp. 91 - 129

In view of the minimization of a nonsmooth nonconvex function f, we prove an abstract convergence result for descent methods satisfying a sufficient-decrease...

Tame optimization | 65K15 | Theoretical, Mathematical and Computational Physics | Alternating minimization | Mathematics | Forward–backward splitting | Descent methods | 90C53 | Mathematical Methods in Physics | Iterative thresholding | Calculus of Variations and Optimal Control; Optimization | Proximal algorithms | Sufficient decrease | Combinatorics | 47J25 | Kurdyka–Łojasiewicz inequality | o-minimal structures | Nonconvex nonsmooth optimization | 34G25 | Semi-algebraic optimization | 47J30 | Mathematics of Computing | 90C25 | Numerical Analysis | Block-coordinate methods | Relative error | 49M15 | 49M37 | 47J35 | Kurdyka-Łojasiewicz inequality | Forward-backward splitting | MATHEMATICS, APPLIED | Kurdyka-Lojasiewicz inequality | GRADIENT-LIKE SYSTEMS | EVOLUTION-EQUATIONS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | SETS | OPTIMIZATION | PROJECTIONS | POINT ALGORITHM | Methods | Algorithms | Studies | Data smoothing | Analysis | Optimization | Mathematical programming | Splitting | Gauss-Seidel method | Mathematical analysis | Minimization | Descent | Convergence

Tame optimization | 65K15 | Theoretical, Mathematical and Computational Physics | Alternating minimization | Mathematics | Forward–backward splitting | Descent methods | 90C53 | Mathematical Methods in Physics | Iterative thresholding | Calculus of Variations and Optimal Control; Optimization | Proximal algorithms | Sufficient decrease | Combinatorics | 47J25 | Kurdyka–Łojasiewicz inequality | o-minimal structures | Nonconvex nonsmooth optimization | 34G25 | Semi-algebraic optimization | 47J30 | Mathematics of Computing | 90C25 | Numerical Analysis | Block-coordinate methods | Relative error | 49M15 | 49M37 | 47J35 | Kurdyka-Łojasiewicz inequality | Forward-backward splitting | MATHEMATICS, APPLIED | Kurdyka-Lojasiewicz inequality | GRADIENT-LIKE SYSTEMS | EVOLUTION-EQUATIONS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | SETS | OPTIMIZATION | PROJECTIONS | POINT ALGORITHM | Methods | Algorithms | Studies | Data smoothing | Analysis | Optimization | Mathematical programming | Splitting | Gauss-Seidel method | Mathematical analysis | Minimization | Descent | Convergence

Journal Article

2017, 1, ISBN 9781498763622, Volume 1, xiv, 347 pages

Iterative processes are the tools used to generate sequences approximating solutions of equations describing real life problems. Intended for researchers in...

Iterative methods (Mathematics) | Numerical analysis | Applied Mathematics | Differential Equations | Computational Numerical Analysis

Iterative methods (Mathematics) | Numerical analysis | Applied Mathematics | Differential Equations | Computational Numerical Analysis

Book

IEEE Transactions on Automatic Control, ISSN 0018-9286, 05/2014, Volume 59, Issue 5, pp. 1131 - 1146

We study distributed optimization problems when N nodes minimize the sum of their individual costs subject to a common vector variable. The costs are convex,...

Algorithm design and analysis | Nesterov gradient | Gradient methods | distributed optimization | Educational institutions | Vectors | Acceleration | convergence rate | Consensus | Convergence | OPTIMIZATION | ALGORITHMS | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Stochastic analysis | Innovations | Convex functions | Evolutionary algorithms | Mathematical optimization | Iterative methods (Mathematics) | Errors | Costs | Algorithms | Mathematical analysis | Constants | Syntax | Optimization

Algorithm design and analysis | Nesterov gradient | Gradient methods | distributed optimization | Educational institutions | Vectors | Acceleration | convergence rate | Consensus | Convergence | OPTIMIZATION | ALGORITHMS | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Stochastic analysis | Innovations | Convex functions | Evolutionary algorithms | Mathematical optimization | Iterative methods (Mathematics) | Errors | Costs | Algorithms | Mathematical analysis | Constants | Syntax | Optimization

Journal Article

2017, Monographs and research notes in mathematics, ISBN 1498758967

Web Resource

1993, Pitman research notes in mathematics series, ISBN 0582234352, Volume 294, 161

Book

Journal of Clinical Epidemiology, ISSN 0895-4356, 05/2018, Volume 97, pp. 39 - 48

This paper updates previous Cochrane guidance on question formulation, searching, and protocol development, reflecting recent developments in methods for...

Systematic reviews | Cochrane collaboration | Question formulation | Qualitative evidence synthesis | Methods | Protocol development | INFORMATION | MODEL | COMPLEX INTERVENTIONS | CONTEXT | STRATEGIES | IMPACT | PUBLIC, ENVIRONMENTAL & OCCUPATIONAL HEALTH | HEALTH CARE SCIENCES & SERVICES | INCLUSION | HEALTH | PARTICIPATION | Medicine, Experimental | Medical research | Social aspects | Epidemiology | Analysis | Qualitative research | Intervention | Problems | Theory | Decision making | Searching | Feasibility studies | Systematic review | Mapping | Feasibility | Iterative methods | Complexity | Index Medicus

Systematic reviews | Cochrane collaboration | Question formulation | Qualitative evidence synthesis | Methods | Protocol development | INFORMATION | MODEL | COMPLEX INTERVENTIONS | CONTEXT | STRATEGIES | IMPACT | PUBLIC, ENVIRONMENTAL & OCCUPATIONAL HEALTH | HEALTH CARE SCIENCES & SERVICES | INCLUSION | HEALTH | PARTICIPATION | Medicine, Experimental | Medical research | Social aspects | Epidemiology | Analysis | Qualitative research | Intervention | Problems | Theory | Decision making | Searching | Feasibility studies | Systematic review | Mapping | Feasibility | Iterative methods | Complexity | Index Medicus

Journal Article

2010, London Mathematical Society lecture note series, ISBN 9780521438001, Volume 371., x, 354

This is a one-stop introduction to the methods of ergodic theory applied to holomorphic iteration. The authors begin with introductory chapters presenting the...

Ergodic theory | Fractals | Conformal geometry | Iterative methods (Mathematics)

Ergodic theory | Fractals | Conformal geometry | Iterative methods (Mathematics)

Book

2014, De Gruyter studies in mathematics, ISBN 9783110329674, Volume 56, 57., 2 v.

Book

2011, Chapman & Hall/CRC numerical analysis and scientific computing, ISBN 9781439869826, xxiii, 303

Book

2013, 1, ISBN 9780123970138, xiii, 299

This book is the first on the topic and explains the most cutting-edge methods needed for precise calculations and explores the development of powerful...

Differential equations, Nonlinear | Numerical solutions | Mathematics | Differential equations, Nonlinear - Numerical solutions | Math | Iterative methods (Mathematics)

Differential equations, Nonlinear | Numerical solutions | Mathematics | Differential equations, Nonlinear - Numerical solutions | Math | Iterative methods (Mathematics)

Book

1983, Topics in computer mathematics, ISBN 9780677163208, Volume 1, xi, 556

Book

International Journal for Numerical Methods in Engineering, ISSN 0029-5981, 2001, Volume 50, Issue 7, pp. 1523 - 1544

The FETI method and its two-level extension (FETI-2) are two numerically scalable domain decomposition methods with Lagrange multipliers for the iterative...

Iterative methods | Domain decomposition | Numerical scalability | iterative methods | MATHEMATICS, APPLIED | ITERATIVE SOLVERS | numerical scalability | domain decomposition | ALGORITHM | LAGRANGE MULTIPLIERS | EXTENSION | DOMAIN DECOMPOSITION METHOD | SUBSTRUCTURING METHOD | ENGINEERING, MULTIDISCIPLINARY | CONVERGENCE | SYSTEMS | PARALLEL SOLUTION

Iterative methods | Domain decomposition | Numerical scalability | iterative methods | MATHEMATICS, APPLIED | ITERATIVE SOLVERS | numerical scalability | domain decomposition | ALGORITHM | LAGRANGE MULTIPLIERS | EXTENSION | DOMAIN DECOMPOSITION METHOD | SUBSTRUCTURING METHOD | ENGINEERING, MULTIDISCIPLINARY | CONVERGENCE | SYSTEMS | PARALLEL SOLUTION

Journal Article

Computer Physics Communications, ISSN 0010-4655, 01/2019, Volume 234, Issue C, pp. 278 - 285

We present the Alternating Anderson–Richardson (AAR) method: an efficient and scalable alternative to preconditioned Krylov solvers for the solution of large,...

Linear systems of equations | Anderson extrapolation | Parallel computing | Richardson iteration | Electronic structure calculations | PARALLEL IMPLEMENTATION | ALGORITHM | JACOBI ITERATIVE METHOD | PHYSICS, MATHEMATICAL | GLOBAL COMMUNICATION | CONVERGENCE ACCELERATION | FINITE-DIFFERENCE FORMULATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CLUSTERS | GMRES | DENSITY-FUNCTIONAL THEORY | Linear systems | Multiprocessing | Methods | MATHEMATICS AND COMPUTING

Linear systems of equations | Anderson extrapolation | Parallel computing | Richardson iteration | Electronic structure calculations | PARALLEL IMPLEMENTATION | ALGORITHM | JACOBI ITERATIVE METHOD | PHYSICS, MATHEMATICAL | GLOBAL COMMUNICATION | CONVERGENCE ACCELERATION | FINITE-DIFFERENCE FORMULATION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CLUSTERS | GMRES | DENSITY-FUNCTIONAL THEORY | Linear systems | Multiprocessing | Methods | MATHEMATICS AND COMPUTING

Journal Article

1994, Topics in computer mathematics, ISBN 2881249566, Volume 4., xi, 491

Book

Mathematical Programming, ISSN 0025-5610, 8/2013, Volume 140, Issue 1, pp. 125 - 161

In this paper we analyze several new methods for solving optimization problems with the objective function formed as a sum of two terms: one is smooth and...

68Q25 | Theoretical, Mathematical and Computational Physics | Mathematics | Complexity theory | Black-box model | Local optimization | l_1$$ -Regularization | Mathematical Methods in Physics | Optimal methods | Structural optimization | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | 90C47 | Numerical Analysis | Convex Optimization | Nonsmooth optimization | Combinatorics | 1-Regularization | MATHEMATICS, APPLIED | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | DECONVOLUTION | MINIMIZATION | l-Regularization | Studies | Mathematical models | Optimization | Mathematical programming | Composite functions | Computation | Mathematical analysis | Iterative methods | Descent | Convergence

68Q25 | Theoretical, Mathematical and Computational Physics | Mathematics | Complexity theory | Black-box model | Local optimization | l_1$$ -Regularization | Mathematical Methods in Physics | Optimal methods | Structural optimization | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | 90C47 | Numerical Analysis | Convex Optimization | Nonsmooth optimization | Combinatorics | 1-Regularization | MATHEMATICS, APPLIED | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | DECONVOLUTION | MINIMIZATION | l-Regularization | Studies | Mathematical models | Optimization | Mathematical programming | Composite functions | Computation | Mathematical analysis | Iterative methods | Descent | Convergence

Journal Article

1999, Frontiers in applied mathematics, ISBN 9780898714333, xv, 180

Book

2017, ISBN 9781498763622

Web Resource

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