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

IEEE Transactions on Cybernetics, ISSN 2168-2267, 05/2017, Volume 47, Issue 5, pp. 1224 - 1237

In this paper, a novel discrete-time deterministic Q-learning algorithm is developed. In each iteration of the developed Q-learning algorithm, the iterative Q...

Discrete-time systems | Algorithm design and analysis | approximate dynamic programming | neural networks (NNs) | Neural networks | Optimal control | Iterative algorithms | Dynamic programming | neuro-dynamic programming | Adaptive critic designs | adaptive dynamic programming (ADP) | Q -learning"> Q -learning | Q-learning | optimal control | DESIGN | APPROXIMATION | ZERO-SUM GAMES | INPUT-OUTPUT DATA | ALGORITHM | REPRESENTATION | OPTIMAL TRACKING CONTROL | DEAD-ZONE INPUT | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, CYBERNETICS | H-INFINITY CONTROL | NONLINEAR-SYSTEMS | Lower bounds | Algorithms | Computer simulation | Machine learning | Criteria | Iterative methods | Acquisitions & mergers | Convergence

Discrete-time systems | Algorithm design and analysis | approximate dynamic programming | neural networks (NNs) | Neural networks | Optimal control | Iterative algorithms | Dynamic programming | neuro-dynamic programming | Adaptive critic designs | adaptive dynamic programming (ADP) |

Journal Article

Mathematical Programming, ISSN 0025-5610, 9/2016, Volume 159, Issue 1, pp. 253 - 287

We revisit the proofs of convergence for a first order primal–dual algorithm for convex optimization which we have studied a few years ago. In particular, we...

Theoretical, Mathematical and Computational Physics | Convergence rates | Ergodic convergence | Mathematics | 65Y20 | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | 49M29 | First order algorithms | 65K10 | Combinatorics | Saddle-point problems | Primal–dual algorithms | BREGMAN FUNCTIONS | MATHEMATICS, APPLIED | Primal-dual algorithms | MAXIMAL MONOTONE-OPERATORS | PROXIMAL METHOD | INCLUSIONS | CONVEX-OPTIMIZATION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | MAPPINGS | Graphics software | Algorithms | Studies | Mathematical analysis | Mathematical programming | Computational geometry | Operators | Proving | Norms | Nonlinearity | Optimization | Convergence

Theoretical, Mathematical and Computational Physics | Convergence rates | Ergodic convergence | Mathematics | 65Y20 | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | 49M29 | First order algorithms | 65K10 | Combinatorics | Saddle-point problems | Primal–dual algorithms | BREGMAN FUNCTIONS | MATHEMATICS, APPLIED | Primal-dual algorithms | MAXIMAL MONOTONE-OPERATORS | PROXIMAL METHOD | INCLUSIONS | CONVEX-OPTIMIZATION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | MAPPINGS | Graphics software | Algorithms | Studies | Mathematical analysis | Mathematical programming | Computational geometry | Operators | Proving | Norms | Nonlinearity | Optimization | Convergence

Journal Article

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 4/2018, Volume 57, Issue 2, pp. 1 - 23

In this note we prove in the nonlinear setting of $${{\mathrm{CD}}}(K,\infty )$$ CD(K,∞) spaces the stability of the Krasnoselskii spectrum of the Laplace...

49J35 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | 49J52 | 49R05 | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | 58J35 | METRIC-MEASURE-SPACES | MATHEMATICS | MATHEMATICS, APPLIED | MANIFOLDS | RICCI CURVATURE

49J35 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | 49J52 | 49R05 | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics | 58J35 | METRIC-MEASURE-SPACES | MATHEMATICS | MATHEMATICS, APPLIED | MANIFOLDS | RICCI CURVATURE

Journal Article

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 12/2018, Volume 57, Issue 6, pp. 1 - 46

We introduce the concept of nonlocal H-convergence. For this we employ the theory of abstract closed complexes of operators in Hilbert spaces. We show...

Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 74Q05 | 35L04 | Mathematics | Secondary 74Q10 | 35J58 | 35M33 | 35Q61 | Primary 35B27 | MATHEMATICS | MATHEMATICS, APPLIED | ELECTROMAGNETIC THEORY | PERSPECTIVE | FRACTIONAL ELASTICITY | HETEROGENEOUS MEDIA | BOUNDARY-VALUE-PROBLEMS | LIPSCHITZ-DOMAINS | MATERIAL LAWS | MAXWELLS EQUATIONS | HOMOGENIZATION | Quantum theory

Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 74Q05 | 35L04 | Mathematics | Secondary 74Q10 | 35J58 | 35M33 | 35Q61 | Primary 35B27 | MATHEMATICS | MATHEMATICS, APPLIED | ELECTROMAGNETIC THEORY | PERSPECTIVE | FRACTIONAL ELASTICITY | HETEROGENEOUS MEDIA | BOUNDARY-VALUE-PROBLEMS | LIPSCHITZ-DOMAINS | MATERIAL LAWS | MAXWELLS EQUATIONS | HOMOGENIZATION | Quantum theory

Journal Article

Econometrica, ISSN 0012-9682, 1/2015, Volume 83, Issue 1, pp. 353 - 373

In this paper, I construct players' prior beliefs and show that these prior beliefs lead the players to learn to play an approximate Nash equilibrium uniformly...

Learning | Outcomes of education | Theater | NOTES AND COMMENTS | Repeated games | Steepest descent method | Games | Nash equilibrium | Statistical tests | Game theory | Probabilities | smooth approximate optimal behavior | learning to predict strategies | convergence | Bayesian learning | ε-Nash equilibrium | Smooth approximate optimal behavior | η-learning to predict strategies | Convergence | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | REPEATED GAMES | INCOMPLETE INFORMATION | HYPOTHESIS | epsilon-Nash equilibrium | eta-learning to predict strategies | STATISTICS & PROBABILITY | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS

Learning | Outcomes of education | Theater | NOTES AND COMMENTS | Repeated games | Steepest descent method | Games | Nash equilibrium | Statistical tests | Game theory | Probabilities | smooth approximate optimal behavior | learning to predict strategies | convergence | Bayesian learning | ε-Nash equilibrium | Smooth approximate optimal behavior | η-learning to predict strategies | Convergence | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | REPEATED GAMES | INCOMPLETE INFORMATION | HYPOTHESIS | epsilon-Nash equilibrium | eta-learning to predict strategies | STATISTICS & PROBABILITY | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS

Journal Article

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 12/2015, Volume 297, pp. 292 - 324

This paper presents a method for isogeometric analysis using rational Triangular Bézier Splines (rTBS) where optimal convergence rates are achieved. In this...

Isogeometric analysis | Optimal convergence rate | Triangular Bézier spline | Geometric map | Triangular Bézier spline | SHAPE OPTIMIZATION | Triangular Bezier spline | B-SPLINES | APPROXIMATION | SPACES | T-SPLINES | BIVARIATE SPLINES | NURBS | REFINEMENT | INTERPOLATION | NUMERICAL-SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY

Isogeometric analysis | Optimal convergence rate | Triangular Bézier spline | Geometric map | Triangular Bézier spline | SHAPE OPTIMIZATION | Triangular Bezier spline | B-SPLINES | APPROXIMATION | SPACES | T-SPLINES | BIVARIATE SPLINES | NURBS | REFINEMENT | INTERPOLATION | NUMERICAL-SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 8/2019, Volume 182, Issue 2, pp. 606 - 639

Over the past decades, operator splitting methods have become ubiquitous for non-smooth optimization owing to their simplicity and efficiency. In this paper,...

Forward–Backward | 65K05 | Mathematics | Theory of Computation | Bregman distance | Optimization | Finite identification | Partial smoothness | Calculus of Variations and Optimal Control; Optimization | 49J52 | 90C25 | Operations Research/Decision Theory | Forward–Douglas–Rachford | 65K10 | Applications of Mathematics | Engineering, general | Local linear convergence | MATHEMATICS, APPLIED | SMOOTHNESS | ALGORITHM | Forward-Douglas-Rachford | DESCENT METHODS | Forward-Backward | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ERROR-BOUNDS | CONVEX MINIMIZATION | Analysis | Methods | Machine learning | Operators (mathematics) | Manifolds | Economic models | Splitting | Divergence | Inverse problems | Image processing | Signal processing | Iterative methods | Convergence | Signal and Image Processing | Information Theory | Functional Analysis | Numerical Analysis | Computer Science | Optimization and Control | Statistics | Statistics Theory | Machine Learning

Forward–Backward | 65K05 | Mathematics | Theory of Computation | Bregman distance | Optimization | Finite identification | Partial smoothness | Calculus of Variations and Optimal Control; Optimization | 49J52 | 90C25 | Operations Research/Decision Theory | Forward–Douglas–Rachford | 65K10 | Applications of Mathematics | Engineering, general | Local linear convergence | MATHEMATICS, APPLIED | SMOOTHNESS | ALGORITHM | Forward-Douglas-Rachford | DESCENT METHODS | Forward-Backward | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ERROR-BOUNDS | CONVEX MINIMIZATION | Analysis | Methods | Machine learning | Operators (mathematics) | Manifolds | Economic models | Splitting | Divergence | Inverse problems | Image processing | Signal processing | Iterative methods | Convergence | Signal and Image Processing | Information Theory | Functional Analysis | Numerical Analysis | Computer Science | Optimization and Control | Statistics | Statistics Theory | Machine Learning

Journal Article

The Annals of Statistics, ISSN 0090-5364, 8/2010, Volume 38, Issue 4, pp. 2118 - 2144

Covariance matrix plays a central role in multivariate statistical analysis. Significant advances have been made recently on developing both theory and...

Minimax | Maximum likelihood estimation | Gaussian distributions | Analytical estimating | Eigenvalues | Maximum likelihood estimators | Mathematical vectors | Covariance matrices | Estimators | Estimation methods | Tapering | Covariance matrix | Minimax lower bound | Optimal rate of convergence | Frobenius norm | Operator norm | minimax lower bound | SPARSITY | optimal rate of convergence | operator norm | STATISTICS & PROBABILITY | tapering | SELECTION | 62G09 | 62F12 | 62H12

Minimax | Maximum likelihood estimation | Gaussian distributions | Analytical estimating | Eigenvalues | Maximum likelihood estimators | Mathematical vectors | Covariance matrices | Estimators | Estimation methods | Tapering | Covariance matrix | Minimax lower bound | Optimal rate of convergence | Frobenius norm | Operator norm | minimax lower bound | SPARSITY | optimal rate of convergence | operator norm | STATISTICS & PROBABILITY | tapering | SELECTION | 62G09 | 62F12 | 62H12

Journal Article

IEEE Transactions on Cybernetics, ISSN 2168-2267, 12/2014, Volume 44, Issue 12, pp. 2733 - 2743

Value iteration-based approximate/adaptive dynamic programming (ADP) as an approximate solution to infinite-horizon optimal control problems with deterministic...

Optimal control | nonlinear control systems | Approximate dynamic programming | Vectors | Dynamic programming | Approximation methods | Mathematical model | Equations | Convergence | optimal control | TIME NONLINEAR-SYSTEMS | AUTOMATION & CONTROL SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, CYBERNETICS | Optimization | Learning | Policies | Approximation | Mathematical analysis | Mathematical models | Iterative methods

Optimal control | nonlinear control systems | Approximate dynamic programming | Vectors | Dynamic programming | Approximation methods | Mathematical model | Equations | Convergence | optimal control | TIME NONLINEAR-SYSTEMS | AUTOMATION & CONTROL SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, CYBERNETICS | Optimization | Learning | Policies | Approximation | Mathematical analysis | Mathematical models | Iterative methods

Journal Article

Mathematical Programming, ISSN 0025-5610, 9/2016, Volume 159, Issue 1, pp. 403 - 434

In this paper, we present a convergence rate analysis for the inexact Krasnosel’skiĭ–Mann iteration built from non-expansive operators. The presented results...

Monotone inclusion | Theoretical, Mathematical and Computational Physics | Convergence rates | Non-expansive operator | Asymptotic regularity | Mathematics | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Convex optimization | 90C25 | Numerical Analysis | Krasnosel’skiĭ–Mann iteration | 47H09 | Combinatorics | 47H05 | MATHEMATICS, APPLIED | Krasnosel'skii-Mann iteration | PROXIMAL POINT ALGORITHM | SUM | EXTRAGRADIENT | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MONOTONE INCLUSIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | REGULARITY | WEAK-CONVERGENCE | CONVEX MINIMIZATION | Studies | Mathematical analysis | Asymptotic methods | Optimization | Convergence | Mathematical programming | Operators (mathematics) | Operators | Splitting | Approximation | Criteria | Iterative methods

Monotone inclusion | Theoretical, Mathematical and Computational Physics | Convergence rates | Non-expansive operator | Asymptotic regularity | Mathematics | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Convex optimization | 90C25 | Numerical Analysis | Krasnosel’skiĭ–Mann iteration | 47H09 | Combinatorics | 47H05 | MATHEMATICS, APPLIED | Krasnosel'skii-Mann iteration | PROXIMAL POINT ALGORITHM | SUM | EXTRAGRADIENT | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MONOTONE INCLUSIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | REGULARITY | WEAK-CONVERGENCE | CONVEX MINIMIZATION | Studies | Mathematical analysis | Asymptotic methods | Optimization | Convergence | Mathematical programming | Operators (mathematics) | Operators | Splitting | Approximation | Criteria | Iterative methods

Journal Article

Mathematical Programming, ISSN 0025-5610, 3/2017, Volume 162, Issue 1, pp. 165 - 199

We analyze the convergence rate of the alternating direction method of multipliers (ADMM) for minimizing the sum of two or more nonsmooth convex separable...

Mathematical Methods in Physics | Linear convergence | Dual ascent | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Alternating directions of multipliers | Error bound | Mathematics | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | STRICTLY CONVEX COSTS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | INEQUALITIES | RELAXATION METHODS | DUAL ASCENT METHODS | SPLITTING ALGORITHMS | Analysis | Methods | Algorithms | Studies | Linear programming | Errors | Multipliers | Mathematical analysis | Texts | Feasibility | Mathematical models | Convexity | Convergence

Mathematical Methods in Physics | Linear convergence | Dual ascent | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Alternating directions of multipliers | Error bound | Mathematics | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | STRICTLY CONVEX COSTS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | INEQUALITIES | RELAXATION METHODS | DUAL ASCENT METHODS | SPLITTING ALGORITHMS | Analysis | Methods | Algorithms | Studies | Linear programming | Errors | Multipliers | Mathematical analysis | Texts | Feasibility | Mathematical models | Convexity | Convergence

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 06/2018, Volume 326, pp. 87 - 104

In this paper, we analyze the convergence and semi-convergence of a class of SSOR-like methods with four real functions for augmented systems. The class takes...

The minimum of convergence factors | SSOR-like methods | Semi-convergence | Convergence | SUCCESSIVE OVERRELAXATION | MATHEMATICS, APPLIED | INEXACT UZAWA ALGORITHM | CONSTRAINT PRECONDITIONERS | ITERATIVE METHOD | HERMITIAN SPLITTING METHODS | NUMERICAL-SOLUTION | SYMMETRIC SOR METHOD | GSOR-LIKE METHODS | AOR METHOD | OPTIMAL PARAMETERS

The minimum of convergence factors | SSOR-like methods | Semi-convergence | Convergence | SUCCESSIVE OVERRELAXATION | MATHEMATICS, APPLIED | INEXACT UZAWA ALGORITHM | CONSTRAINT PRECONDITIONERS | ITERATIVE METHOD | HERMITIAN SPLITTING METHODS | NUMERICAL-SOLUTION | SYMMETRIC SOR METHOD | GSOR-LIKE METHODS | AOR METHOD | OPTIMAL PARAMETERS

Journal Article

IEEE Transactions on Fuzzy Systems, ISSN 1063-6706, 12/2013, Volume 21, Issue 6, pp. 1123 - 1132

In this paper, an enhanced adaptive fuzzy control (AFC) strategy with guaranteed convergence of an optimal fuzzy approximation error (FAE) is presented for a...

uncertain nonlinear system | Vectors | Approximation methods | Adaptive control | Frequency control | Convergence | high-precision tracking | fuzzy control | Asymptotic stability | asymptotically stable | optimal approximation error convergence | Closed loop systems | Nonlinear systems | Fuzzy control | Uncertain nonlinear system | Asymptotically stable | Optimal approximation error convergence | High-precision tracking | VARIABLE UNIVERSE | OUTPUT-FEEDBACK CONTROL | UNCERTAIN NONLINEAR-SYSTEMS | ROBOT MANIPULATORS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | NEURAL-NETWORK | INFINITY TRACKING CONTROL

uncertain nonlinear system | Vectors | Approximation methods | Adaptive control | Frequency control | Convergence | high-precision tracking | fuzzy control | Asymptotic stability | asymptotically stable | optimal approximation error convergence | Closed loop systems | Nonlinear systems | Fuzzy control | Uncertain nonlinear system | Asymptotically stable | Optimal approximation error convergence | High-precision tracking | VARIABLE UNIVERSE | OUTPUT-FEEDBACK CONTROL | UNCERTAIN NONLINEAR-SYSTEMS | ROBOT MANIPULATORS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | NEURAL-NETWORK | INFINITY TRACKING CONTROL

Journal Article

The Annals of Statistics, ISSN 0090-5364, 10/2012, Volume 40, Issue 5, pp. 2389 - 2420

This paper considers estimation of sparse covariance matrices and establishes the optimal rate of convergence under a range of matrix operator norm and Bregman...

Minimax | Threshing | Eigenvalues | Mathematical vectors | Mathematics | Covariance matrices | Estimators | Uniformity | Estimation methods | Perceptron convergence procedure | Spectral norm | Bregman divergence | Optimal rate of convergence | Thresholding | Frobenius norm | Assouad's lemma | Covariance matrix estimation | Le Cam's method | Minimax lower bound | minimax lower bound | thresholding | spectral norm | optimal rate of convergence | STATISTICS & PROBABILITY | covariance matrix estimation | 62G09 | 62F12 | Le Cam’s method | Assouad’s lemma | 62H12

Minimax | Threshing | Eigenvalues | Mathematical vectors | Mathematics | Covariance matrices | Estimators | Uniformity | Estimation methods | Perceptron convergence procedure | Spectral norm | Bregman divergence | Optimal rate of convergence | Thresholding | Frobenius norm | Assouad's lemma | Covariance matrix estimation | Le Cam's method | Minimax lower bound | minimax lower bound | thresholding | spectral norm | optimal rate of convergence | STATISTICS & PROBABILITY | covariance matrix estimation | 62G09 | 62F12 | Le Cam’s method | Assouad’s lemma | 62H12

Journal Article

SIAM Journal on Numerical Analysis, ISSN 0036-1429, 1/2008, Volume 46, Issue 5, pp. 2524 - 2550

We analyze the simplest and most standard adaptive finite element method (AFEM), with any polynomial degree, for general second order linear, symmetric...

Finite element method | Triangulation | Approximation | A posteriori knowledge | Cardinality | Polynomials | Conformity | Estimators | Degrees of polynomials | Adaptive algorithm | Optimal cardinality | Error reduction | Convergence | optimal cardinality | DIMENSIONS | MATHEMATICS, APPLIED | error reduction | convergence | BOUNDARY-CONDITIONS | MESH REFINEMENT | ALGORITHM | adaptive algorithm | BISECTION

Finite element method | Triangulation | Approximation | A posteriori knowledge | Cardinality | Polynomials | Conformity | Estimators | Degrees of polynomials | Adaptive algorithm | Optimal cardinality | Error reduction | Convergence | optimal cardinality | DIMENSIONS | MATHEMATICS, APPLIED | error reduction | convergence | BOUNDARY-CONDITIONS | MESH REFINEMENT | ALGORITHM | adaptive algorithm | BISECTION

Journal Article