Foundations of Computational Mathematics, ISSN 1615-3375, 10/2013, Volume 13, Issue 5, pp. 819 - 834

We consider the problem of reconstructing an unknown function f on a domain X from samples of f at n randomly chosen points with respect to a given measure ρ X...

Economics general | 62J05 | Polynomial approximation | Linear and Multilinear Algebras, Matrix Theory | Mathematics | Random matrices | Numerical Analysis | 93E24 | 65D10 | 42A10 | Least squares | Applications of Mathematics | Math Applications in Computer Science | Computer Science, general | Sampling | 42C05 | MATHEMATICS | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS | Approximation theory | Research | Mathematical research | Polynomials | Computational mathematics | Approximations | Accuracy | Stability | Approximation | Least squares method | Mathematical analysis | Mathematical models | Criteria

Economics general | 62J05 | Polynomial approximation | Linear and Multilinear Algebras, Matrix Theory | Mathematics | Random matrices | Numerical Analysis | 93E24 | 65D10 | 42A10 | Least squares | Applications of Mathematics | Math Applications in Computer Science | Computer Science, general | Sampling | 42C05 | MATHEMATICS | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS | Approximation theory | Research | Mathematical research | Polynomials | Computational mathematics | Approximations | Accuracy | Stability | Approximation | Least squares method | Mathematical analysis | Mathematical models | Criteria

Journal Article

2004, Wiley series in probability and statistics, ISBN 9780470866979, 314

"Generalised Least Squares" adopts a concise and mathematically rigorous approach. It will provide an up-to-date self-contained introduction to the unified...

Least squares | Mathematics | Probability & Statistics | General

Least squares | Mathematics | Probability & Statistics | General

eBook

Journal of the American Statistical Association, ISSN 0162-1459, 09/2007, Volume 102, Issue 479, pp. 1039 - 1048

We propose a method of least squares approximation (LSA) for unified yet simple LASSO estimation. Our general theoretical framework includes ordinary least...

Bayes information criterion | Microarray data | LASSO | Least angle regression | Solution path | Oracle Property | Least squares approximation | Adaptive LASSO | Approximation | Covariance | Objective functions | Theory and Methods | Least squares | Covariance matrices | Modeling | Estimators | Latent semantic analysis | Oracles | Estimation methods | Oracle property | solution path | REGRESSION | microarray data | adaptive LASSO | oracle property | CLASSIFICATION | STATISTICS & PROBABILITY | least squares approximation | least angle regression | VARIABLE SELECTION | ORACLE PROPERTIES | CENSORED-DATA | SHRINKAGE | MODEL SELECTION | ASYMPTOTICS | Models | Algorithms | Analysis

Bayes information criterion | Microarray data | LASSO | Least angle regression | Solution path | Oracle Property | Least squares approximation | Adaptive LASSO | Approximation | Covariance | Objective functions | Theory and Methods | Least squares | Covariance matrices | Modeling | Estimators | Latent semantic analysis | Oracles | Estimation methods | Oracle property | solution path | REGRESSION | microarray data | adaptive LASSO | oracle property | CLASSIFICATION | STATISTICS & PROBABILITY | least squares approximation | least angle regression | VARIABLE SELECTION | ORACLE PROPERTIES | CENSORED-DATA | SHRINKAGE | MODEL SELECTION | ASYMPTOTICS | Models | Algorithms | Analysis

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 07/2015, Volume 282, pp. 237 - 250

In this article the error estimation of the moving least squares approximation is provided for functions in fractional order Sobolev spaces. The analysis...

Error bounds | Moving least squares approximation | Sobolev spaces | Meshless methods | INTERPOLATION | MATHEMATICS, APPLIED | SPACES | ERROR ANALYSIS | Mathematics - Numerical Analysis

Error bounds | Moving least squares approximation | Sobolev spaces | Meshless methods | INTERPOLATION | MATHEMATICS, APPLIED | SPACES | ERROR ANALYSIS | Mathematics - Numerical Analysis

Journal Article

Engineering Analysis with Boundary Elements, ISSN 0955-7997, 01/2015, Volume 50, pp. 249 - 257

This paper proposes an approach based on the Galerkin weak form and moving least squares (MLS) approximation to simulate three space dimensional nonlinear wave...

Three-dimensional wave equation | Moving least squares (MLS) | Local weak formulation | Meshless local Petrov–Galerkin (MLPG) method | Meshless local Petrov-Galerkin (MLPG) method | MESHFREE METHOD | POINT INTERPOLATION METHOD | HYPERBOLIC EQUATION | SINE-GORDON EQUATION | FORMULATION | VIBRATION ANALYSES | SCHEME | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | DIFFERENCE | ENGINEERING, MULTIDISCIPLINARY | FINITE-ELEMENT-METHOD | COLLOCATION | Finite element method | Approximation | Least squares method | Mathematical analysis | Meshless methods | Dirichlet problem | Nonlinearity | Three dimensional

Three-dimensional wave equation | Moving least squares (MLS) | Local weak formulation | Meshless local Petrov–Galerkin (MLPG) method | Meshless local Petrov-Galerkin (MLPG) method | MESHFREE METHOD | POINT INTERPOLATION METHOD | HYPERBOLIC EQUATION | SINE-GORDON EQUATION | FORMULATION | VIBRATION ANALYSES | SCHEME | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | DIFFERENCE | ENGINEERING, MULTIDISCIPLINARY | FINITE-ELEMENT-METHOD | COLLOCATION | Finite element method | Approximation | Least squares method | Mathematical analysis | Meshless methods | Dirichlet problem | Nonlinearity | Three dimensional

Journal Article

Archives of Computational Methods in Engineering, ISSN 1134-3060, 1/2019, Volume 26, Issue 1, pp. 61 - 106

Metamodeling, the science of modeling functions observed at a finite number of points, benefits from all auxiliary information it can account for. Function...

Engineering | Mathematical and Computational Engineering | DESIGN | SUPPORT VECTOR REGRESSION | ALGORITHMS | INTERPOLATION | ADJOINT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | MODELS | GLOBAL OPTIMIZATION | LIKELIHOOD-ESTIMATION | COVARIANCE | RESPONSE-SURFACE APPROXIMATION | Radial basis function | Support vector machines | Formulations | Basis functions | Least squares | Metamodels | Mathematical models | Computing time | Weighting functions | Kriging | Modeling and Simulation | Mathematics | Optimization and Control | Computer Science

Engineering | Mathematical and Computational Engineering | DESIGN | SUPPORT VECTOR REGRESSION | ALGORITHMS | INTERPOLATION | ADJOINT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | MODELS | GLOBAL OPTIMIZATION | LIKELIHOOD-ESTIMATION | COVARIANCE | RESPONSE-SURFACE APPROXIMATION | Radial basis function | Support vector machines | Formulations | Basis functions | Least squares | Metamodels | Mathematical models | Computing time | Weighting functions | Kriging | Modeling and Simulation | Mathematics | Optimization and Control | Computer Science

Journal Article

IEEE Transactions on Pattern Analysis and Machine Intelligence, ISSN 0162-8828, 12/2010, Volume 32, Issue 12, pp. 2232 - 2245

The paper presents SwiftSeg, a novel technique for online time series segmentation and piecewise polynomial representation. The segmentation approach is based...

least-squares approximation | Change detection algorithms | Piecewise linear techniques | Piecewise linear approximation | SwiftSeg | Time series | Partitioning algorithms | Runtime | piecewise polynomial representation | Signal processing algorithms | Clustering algorithms | Computer errors | Approximation error | Polynomials | online segmentation | orthogonal polynomials | RECOGNITION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Signal processing | Usage | Approximation theory | Data mining | Analysis | Studies | Windows (intervals) | Approximation | Segmentation | Least squares method | On-line systems | Online | Curvature

least-squares approximation | Change detection algorithms | Piecewise linear techniques | Piecewise linear approximation | SwiftSeg | Time series | Partitioning algorithms | Runtime | piecewise polynomial representation | Signal processing algorithms | Clustering algorithms | Computer errors | Approximation error | Polynomials | online segmentation | orthogonal polynomials | RECOGNITION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Signal processing | Usage | Approximation theory | Data mining | Analysis | Studies | Windows (intervals) | Approximation | Segmentation | Least squares method | On-line systems | Online | Curvature

Journal Article

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 01/2018, Volume 328, pp. 775 - 803

The main aim of the current paper is to propose a new truly meshless numerical technique to solve the one- and two-dimensional elliptic interface problems. The...

Jump boundary conditions | Interpolating stabilized moving least squares approximation | Elliptic interface problems | Meshless method | Complex computational domains | EQUATIONS | DISCONTINUOUS GALERKIN METHOD | FORMULATION | BOUNDARY MIB METHOD | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | COEFFICIENTS | CONVERGENCE | FINITE-ELEMENT-METHOD | MATCHED INTERFACE | Professional soccer

Jump boundary conditions | Interpolating stabilized moving least squares approximation | Elliptic interface problems | Meshless method | Complex computational domains | EQUATIONS | DISCONTINUOUS GALERKIN METHOD | FORMULATION | BOUNDARY MIB METHOD | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | COEFFICIENTS | CONVERGENCE | FINITE-ELEMENT-METHOD | MATCHED INTERFACE | Professional soccer

Journal Article

Applied Mathematical Modelling, ISSN 0307-904X, 08/2017, Volume 48, pp. 153 - 182

•A meshless method is developed for some generalized Klein–Gordon equations.•A convergent iterative scheme is performed to tackle the nonlinearity.•Examples...

Soliton | Nonlinear generalized Klein–Gordon equation | Well-posed moving least squares approximation | Sine-Gordon | Meshless | Convergence | ELEMENT-FREE METHOD | Nonlinear generalized Klein-Gordon equation | WAVE SOLUTIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | FREE METHOD BEFM | FREE GALERKIN METHOD | BOUNDARY NODE METHOD | Analysis | Numerical analysis

Soliton | Nonlinear generalized Klein–Gordon equation | Well-posed moving least squares approximation | Sine-Gordon | Meshless | Convergence | ELEMENT-FREE METHOD | Nonlinear generalized Klein-Gordon equation | WAVE SOLUTIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | FREE METHOD BEFM | FREE GALERKIN METHOD | BOUNDARY NODE METHOD | Analysis | Numerical analysis

Journal Article

Neurocomputing, ISSN 0925-2312, 2002, Volume 48, Issue 1-4, pp. 85 - 105

Least squares support vector machines (LS-SVM) is an SVM version which involves equality instead of inequality constraints and works with a least squares cost...

Ridge regression | Support vector machines | Robust estimation | Sparse approximation | (Weighted) least squares

Ridge regression | Support vector machines | Robust estimation | Sparse approximation | (Weighted) least squares

Journal Article

European Journal of Operational Research, ISSN 0377-2217, 12/2018, Volume 271, Issue 3, pp. 797 - 807

•Smooth alternative to nonparametric segmented concave least squares.•We use a differentiable approximation using smoothly mixing Cobb-Douglas anchor...

OR in banking | Simulation | Nonparametric concave least squares | Bayesian analysis | Segmented least squares | REGRESSION | MANAGEMENT | CAPITALIZATION | MULTILAYER FEEDFORWARD NETWORKS | RISK | DISTANCE FUNCTION | FORMS | COST | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | EUROPEAN BANKING | EFFICIENCY

OR in banking | Simulation | Nonparametric concave least squares | Bayesian analysis | Segmented least squares | REGRESSION | MANAGEMENT | CAPITALIZATION | MULTILAYER FEEDFORWARD NETWORKS | RISK | DISTANCE FUNCTION | FORMS | COST | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | EUROPEAN BANKING | EFFICIENCY

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 10/2015, Volume 298, Issue C, pp. 787 - 800

We discuss the problem of polynomial approximation of multivariate functions using discrete least squares collocation. The problem stems from uncertainty...

Generalized polynomial chaos | Uncertainty quantification | Least squares method | Orthogonal polynomials | DESIGN | DOMAIN | PHYSICS, MATHEMATICAL | CHAOS | PROJECTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | STOCHASTIC COLLOCATION METHOD | PARTIAL-DIFFERENTIAL-EQUATIONS | CHRISTOFFEL FUNCTIONS | EXPANSION | Approximation | Asymptotic properties | Mathematical analysis | Mathematical models | Polynomials | Stems | Quadratures

Generalized polynomial chaos | Uncertainty quantification | Least squares method | Orthogonal polynomials | DESIGN | DOMAIN | PHYSICS, MATHEMATICAL | CHAOS | PROJECTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | STOCHASTIC COLLOCATION METHOD | PARTIAL-DIFFERENTIAL-EQUATIONS | CHRISTOFFEL FUNCTIONS | EXPANSION | Approximation | Asymptotic properties | Mathematical analysis | Mathematical models | Polynomials | Stems | Quadratures

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 09/2016, Volume 72, Issue 6, pp. 1515 - 1531

In this paper, the stability of the moving least squares (MLS) approximation and a stabilized MLS approximation is analyzed theoretically and verified...

Element-free Galerkin method | Condition number | Moving least squares approximation | Stability | Error estimate | Meshless | Approximation | Deterioration | Least squares method | Mathematical analysis | Dirichlet problem | Mathematical models | Galerkin methods

Element-free Galerkin method | Condition number | Moving least squares approximation | Stability | Error estimate | Meshless | Approximation | Deterioration | Least squares method | Mathematical analysis | Dirichlet problem | Mathematical models | Galerkin methods

Journal Article

Journal of the American Statistical Association, ISSN 0162-1459, 09/2001, Volume 96, Issue 455, pp. 939 - 967

In this paper, we introduce nonlinear regularized wavelet estimators for estimating nonparametric regression functions when sampling points are not uniformly...

Wavelets | Asymptotic minimax | Irregular designs | ROSE | Penalized least-squares | Nonquadratic penality functions | Oracle inequalities | Preliminary estimates | Penalty function | Interpolation | Minimax | Approximation | Theory and Methods | Threshing | Least squares | Estimators | Oracles | Estimation methods | REGRESSION | DESIGN | RECONSTRUCTION | asymptotic minimax | STATISTICS & PROBABILITY | MODEL | oracle inequalities | irregular designs | nonquadratic penality functions | L-CURVE | SHRINKAGE | ESTIMATORS | wavelets | penalized least-squares | SELECTION | Nonlinear theories | Research | Mathematical analysis | Analysis

Wavelets | Asymptotic minimax | Irregular designs | ROSE | Penalized least-squares | Nonquadratic penality functions | Oracle inequalities | Preliminary estimates | Penalty function | Interpolation | Minimax | Approximation | Theory and Methods | Threshing | Least squares | Estimators | Oracles | Estimation methods | REGRESSION | DESIGN | RECONSTRUCTION | asymptotic minimax | STATISTICS & PROBABILITY | MODEL | oracle inequalities | irregular designs | nonquadratic penality functions | L-CURVE | SHRINKAGE | ESTIMATORS | wavelets | penalized least-squares | SELECTION | Nonlinear theories | Research | Mathematical analysis | Analysis

Journal Article

MATHEMATICS, ISSN 2227-7390, 05/2019, Volume 7, Issue 5, p. 462

Spline approximation, using both values yi and xi as observations, is of vital importance for engineering geodesy, e.g., for approximation of profiles measured...

MATHEMATICS | KNOT-PLACEMENT | singular dispersion matrix | constrained weighted total least squares (CWTLS) | spline approximation | total least squares (TLS) | MODEL | Gauss-Helmert (GH) model

MATHEMATICS | KNOT-PLACEMENT | singular dispersion matrix | constrained weighted total least squares (CWTLS) | spline approximation | total least squares (TLS) | MODEL | Gauss-Helmert (GH) model

Journal Article

Applied Mathematical Modelling, ISSN 0307-904X, 07/2017, Volume 47, pp. 45 - 62

•Properties, stability and error of the complex moving least squares approximation are analyzed theoretically.•A stabilized complex moving least squares...

Element-free Galerkin method | Complex variable | Moving least squares approximation | Stability | Error estimate | Meshless | KERNEL PARTICLE METHOD | EQUATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | SINE-GORDON | BOUNDARY NODE METHOD

Element-free Galerkin method | Complex variable | Moving least squares approximation | Stability | Error estimate | Meshless | KERNEL PARTICLE METHOD | EQUATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | SINE-GORDON | BOUNDARY NODE METHOD

Journal Article

SIAM Journal on Scientific Computing, ISSN 1064-8275, 2011, Volume 33, Issue 1, pp. 195 - 222

Given a certain function f, various methods have been proposed in the past for addressing the important problem of computing the matrix-vector product f(A)b...

Least squares polynomials | Gaussian process | Sampling | Matrix function | matrix function | least squares polynomials | MATHEMATICS, APPLIED | MATRIX FUNCTIONS | sampling | KRYLOV SUBSPACE METHOD | SYSTEMS | ITERATIVE SOLUTION | COMPUTATION | Studies | Polynomials | Matrix | Normal distribution | Approximations

Least squares polynomials | Gaussian process | Sampling | Matrix function | matrix function | least squares polynomials | MATHEMATICS, APPLIED | MATRIX FUNCTIONS | sampling | KRYLOV SUBSPACE METHOD | SYSTEMS | ITERATIVE SOLUTION | COMPUTATION | Studies | Polynomials | Matrix | Normal distribution | Approximations

Journal Article