IEEE Transactions on Signal Processing, ISSN 1053-587X, 11/2014, Volume 62, Issue 21, pp. 5690 - 5705

In this paper, we study a probabilistically robust transmit optimization problem under imperfect channel state information (CSI) at the transmitter and under...

Array signal processing | outage probability | Imperfect channel state information | MIMO precoder designs | robust optimization | Downlink | Robustness | Vectors | Silicon | Approximation methods | Optimization | multiuser MIMO | MIMO BROADCAST CHANNELS | FINITE RATE FEEDBACK | INEQUALITIES | SYSTEMS | DESIGNS | SUMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Robust statistics | Usage | Analysis | Gaussian processes | Innovations | Signal processing | Approximation theory | Distribution (Probability theory) | Mathematical optimization | Methods | Heuristic | Outages | Uncertainty | Approximation | Quadratic forms | Mathematical analysis | Constrictions | Mathematical models

Array signal processing | outage probability | Imperfect channel state information | MIMO precoder designs | robust optimization | Downlink | Robustness | Vectors | Silicon | Approximation methods | Optimization | multiuser MIMO | MIMO BROADCAST CHANNELS | FINITE RATE FEEDBACK | INEQUALITIES | SYSTEMS | DESIGNS | SUMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Robust statistics | Usage | Analysis | Gaussian processes | Innovations | Signal processing | Approximation theory | Distribution (Probability theory) | Mathematical optimization | Methods | Heuristic | Outages | Uncertainty | Approximation | Quadratic forms | Mathematical analysis | Constrictions | Mathematical models

Journal Article

International Journal for Numerical Methods in Engineering, ISSN 0029-5981, 04/2017, Volume 110, Issue 3, pp. 279 - 300

Summary We present two accurate and efficient numerical schemes for a phase field dendritic crystal growth model, which is derived from the variation of a...

Phase‐field models | Dendritic Crystal Growth | Second Order | Invariant Energy Quadratization | Linear Elliptic Equations | Unconditional Energy Stability | Phase-field models | STABLE SCHEMES | CAHN-HILLIARD EQUATION | ADAPTIVE MESH REFINEMENT | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | SIMULATIONS | FLOWS | Analysis | Models | Numerical analysis | Dendritic crystals | Anisotropy | Quadratic forms | Mathematical analysis | Nonlinearity | Mathematical models | Entropy | Invariants

Phase‐field models | Dendritic Crystal Growth | Second Order | Invariant Energy Quadratization | Linear Elliptic Equations | Unconditional Energy Stability | Phase-field models | STABLE SCHEMES | CAHN-HILLIARD EQUATION | ADAPTIVE MESH REFINEMENT | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | SIMULATIONS | FLOWS | Analysis | Models | Numerical analysis | Dendritic crystals | Anisotropy | Quadratic forms | Mathematical analysis | Nonlinearity | Mathematical models | Entropy | Invariants

Journal Article

Automatica, ISSN 0005-1098, 11/2017, Volume 85, pp. 272 - 292

Block-oriented nonlinear models are popular in nonlinear system identification because of their advantages of being simple to understand and easy to use. Many...

Hammerstein | Wiener–Hammerstein | Hammerstein–Wiener | Wiener | Parallel cascade | Feedback | Linear fractional representation | System identification | Maximum likelihood | Nonlinear systems | Best linear approximation | NONPARAMETRIC IDENTIFICATION | RECURSIVE-IDENTIFICATION | ROBUST STABILITY | Wiener-Hammerstein | ITERATIVE METHOD | MAXIMUM-LIKELIHOOD IDENTIFICATION | ENGINEERING, ELECTRICAL & ELECTRONIC | Hammerstein-Wiener | PARAMETRIC IDENTIFICATION | WIENER-HAMMERSTEIN SYSTEMS | EXPLICIT CONSTRUCTION | QUADRATIC LYAPUNOV FUNCTIONS | AUTOMATION & CONTROL SYSTEMS | BIOLOGICAL-SYSTEMS | Surveys | Algorithms | Computer Science - Systems and Control

Hammerstein | Wiener–Hammerstein | Hammerstein–Wiener | Wiener | Parallel cascade | Feedback | Linear fractional representation | System identification | Maximum likelihood | Nonlinear systems | Best linear approximation | NONPARAMETRIC IDENTIFICATION | RECURSIVE-IDENTIFICATION | ROBUST STABILITY | Wiener-Hammerstein | ITERATIVE METHOD | MAXIMUM-LIKELIHOOD IDENTIFICATION | ENGINEERING, ELECTRICAL & ELECTRONIC | Hammerstein-Wiener | PARAMETRIC IDENTIFICATION | WIENER-HAMMERSTEIN SYSTEMS | EXPLICIT CONSTRUCTION | QUADRATIC LYAPUNOV FUNCTIONS | AUTOMATION & CONTROL SYSTEMS | BIOLOGICAL-SYSTEMS | Surveys | Algorithms | Computer Science - Systems and Control

Journal Article

Journal of Chemical Physics, ISSN 0021-9606, 08/2009, Volume 131, Issue 6, pp. 064103 - 064103-15

A production level implementation of the closed-shell local quadratic configuration interaction and coupled cluster methods with single and double excitations...

QUADRATIC CONFIGURATION-INTERACTION | DENSITY FITTING APPROXIMATIONS | PLESSET PERTURBATION-THEORY | AB-INITIO | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | HARTREE-FOCK | intermolecular mechanics | WAVE-FUNCTIONS | QUANTUM-CHEMISTRY | configuration interactions | coupled cluster calculations | ANALYTICAL ENERGY GRADIENTS | orbital calculations | ELECTRON CORRELATION METHODS | GAUSSIAN-BASIS SETS

QUADRATIC CONFIGURATION-INTERACTION | DENSITY FITTING APPROXIMATIONS | PLESSET PERTURBATION-THEORY | AB-INITIO | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | HARTREE-FOCK | intermolecular mechanics | WAVE-FUNCTIONS | QUANTUM-CHEMISTRY | configuration interactions | coupled cluster calculations | ANALYTICAL ENERGY GRADIENTS | orbital calculations | ELECTRON CORRELATION METHODS | GAUSSIAN-BASIS SETS

Journal Article

Structural and Multidisciplinary Optimization, ISSN 1615-147X, 2010, Volume 41, Issue 1, pp. 39 - 56

We propose to replace a number of popular approximations by their diagonal quadratic Taylor series expansions. The resulting separable quadratic approximations...

Engineering | Computational Mathematics and Numerical Analysis | Global convergence | Conservatism | Intervening variables | Conservative convex separable approximation | Engineering Design | Sequential approximate optimization (SAO) | Theoretical and Applied Mechanics | Diagonal quadratic approximation | Quadratic Taylor expansion | DESIGN | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | STRUCTURAL OPTIMIZATION | Algorithms | Universities and colleges | Mechanical engineering | Mathematical optimization | Taylor series | Asymptotes | Approximation | Mathematical analysis | Optimization

Engineering | Computational Mathematics and Numerical Analysis | Global convergence | Conservatism | Intervening variables | Conservative convex separable approximation | Engineering Design | Sequential approximate optimization (SAO) | Theoretical and Applied Mechanics | Diagonal quadratic approximation | Quadratic Taylor expansion | DESIGN | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | STRUCTURAL OPTIMIZATION | Algorithms | Universities and colleges | Mechanical engineering | Mathematical optimization | Taylor series | Asymptotes | Approximation | Mathematical analysis | Optimization

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 06/2013, Volume 243, pp. 323 - 343

Mathematical models of advection–reaction phenomena rely on advective flow velocity and (bio) chemical reaction rates that are notoriously random. By using...

Uncertainty quantification | Geochemistry | Stochastic modeling | PDF methods | Heterogeneous reaction | REPRESENTATIONS | POLYNOMIAL CHAOS | RANDOMLY HETEROGENEOUS DOMAINS | DECOMPOSITION | TRANSIENT FLOW | DEFINITE QUADRATIC-FORMS | PHYSICS, MATHEMATICAL | DISTRIBUTIONS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CONDITIONAL MOMENT EQUATIONS | Approximation | Mathematical analysis | Flow velocity | Mathematical models | Robustness | Transport | Closures | Probability density functions

Uncertainty quantification | Geochemistry | Stochastic modeling | PDF methods | Heterogeneous reaction | REPRESENTATIONS | POLYNOMIAL CHAOS | RANDOMLY HETEROGENEOUS DOMAINS | DECOMPOSITION | TRANSIENT FLOW | DEFINITE QUADRATIC-FORMS | PHYSICS, MATHEMATICAL | DISTRIBUTIONS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CONDITIONAL MOMENT EQUATIONS | Approximation | Mathematical analysis | Flow velocity | Mathematical models | Robustness | Transport | Closures | Probability density functions

Journal Article

European Journal of Operational Research, ISSN 0377-2217, 03/2017, Volume 257, Issue 2, pp. 395 - 411

•A bilevel algorithm based on approximations of the reaction set mapping is proposed.•Theoretical results in classical bilevel optimization motivate the...

Bilevel optimization | Quadratic approximations | Evolutionary algorithms | LOCATION | LOCAL-SEARCH | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | PROGRAMMING-MODEL | EFFICIENT | FOLLOWER | GENETIC ALGORITHM | Mathematical optimization | Analysis | Algorithms

Bilevel optimization | Quadratic approximations | Evolutionary algorithms | LOCATION | LOCAL-SEARCH | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | PROGRAMMING-MODEL | EFFICIENT | FOLLOWER | GENETIC ALGORITHM | Mathematical optimization | Analysis | Algorithms

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 11/2017, Volume 355, Issue 3, pp. 1189 - 1207

We consider a nonlinear Klein–Gordon equation with a quasilinear quadratic term. The Nonlinear Schrödinger (NLS) equation can be derived as a formal...

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | QUADRATIC RESONANCES | NLS APPROXIMATION | NORMAL FORMS | SYSTEMS | WATER-WAVE PROBLEM | MODEL | PHYSICS, MATHEMATICAL | VALIDITY | MODULATION APPROXIMATION

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | QUADRATIC RESONANCES | NLS APPROXIMATION | NORMAL FORMS | SYSTEMS | WATER-WAVE PROBLEM | MODEL | PHYSICS, MATHEMATICAL | VALIDITY | MODULATION APPROXIMATION

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 12/2015, Volume 290, pp. 268 - 277

Numerical methods for matrix eigenvalue problems that are nonlinear in the eigenvalue parameter are discussed. We propose a successive quadratic approximations...

Successive quadratic approximations | Eigenvector | Nonlinear eigenvalue problem | Linearization | NUMERICAL RECIPES | MATHEMATICS, APPLIED | INVERSE | Sequences | Numerical analysis | Approximation | Computation | Eigenvalues | Nonlinearity | Mathematical models | Convergence

Successive quadratic approximations | Eigenvector | Nonlinear eigenvalue problem | Linearization | NUMERICAL RECIPES | MATHEMATICS, APPLIED | INVERSE | Sequences | Numerical analysis | Approximation | Computation | Eigenvalues | Nonlinearity | Mathematical models | Convergence

Journal Article

Computer-Aided Design, ISSN 0010-4485, 2011, Volume 43, Issue 8, pp. 1011 - 1017

We present a method for G 2 end-point interpolation of offset curves using rational Bézier curves. The method is based on a G 2 end-point interpolation of...

Offset curve | Hausdorff distance | Circle approximation | Convolution curve | Curvature continuous interpolation | Quadratic Bézier biarcs | COMPUTER SCIENCE, SOFTWARE ENGINEERING | RATIONAL OFFSETS | CONVOLUTIONS | Quadratic Bezier biarcs | COMPUTATION | CURVES | SURFACES | Interpolation | Approximation | Mathematical analysis | Bezier | Biarc | Mathematical models | Offsets | Curvature

Offset curve | Hausdorff distance | Circle approximation | Convolution curve | Curvature continuous interpolation | Quadratic Bézier biarcs | COMPUTER SCIENCE, SOFTWARE ENGINEERING | RATIONAL OFFSETS | CONVOLUTIONS | Quadratic Bezier biarcs | COMPUTATION | CURVES | SURFACES | Interpolation | Approximation | Mathematical analysis | Bezier | Biarc | Mathematical models | Offsets | Curvature

Journal Article

International Journal of Electrical Power and Energy Systems, ISSN 0142-0615, 05/2019, Volume 107, pp. 680 - 689

•The presented OPF approximations reflect any grid topology and any voltage levels.•Our methods can be efficiently solved by using off-the-shelf LP/QP...

Optimal power flow | Power flow approximation | Linear/quadratic programming | OPERATIONS | SYSTEMS | RELAXATION | ENGINEERING, ELECTRICAL & ELECTRONIC | Computer Science - Systems and Control

Optimal power flow | Power flow approximation | Linear/quadratic programming | OPERATIONS | SYSTEMS | RELAXATION | ENGINEERING, ELECTRICAL & ELECTRONIC | Computer Science - Systems and Control

Journal Article

Journal of Inequalities and Applications, ISSN 1029-242X, 12/2019, Volume 2019, Issue 1, pp. 1 - 18

In this paper, we provide an estimate for approximating the generalized-Euler-constant function γ(z)=∑k=1∞zk−1(1k−lnk+1k) $\gamma (z)=\sum_{k=1}^{\infty }z...

Somos’ quadratic recurrence constant | Generalized-Euler-constant function | 33E20 | Mathematics | 41A60 | Asymptotic expansion | Analysis | Mathematics, general | 11Y60 | Eulerian fraction | Applications of Mathematics | 26D15 | Inequality | MATHEMATICS | MATHEMATICS, APPLIED | SERIES | ASYMPTOTIC EXPANSIONS | CONVERGENT | PSI FUNCTION | Somos' quadratic recurrence constant | DOUBLE INTEGRALS | Thermal expansion | Asymptotic series

Somos’ quadratic recurrence constant | Generalized-Euler-constant function | 33E20 | Mathematics | 41A60 | Asymptotic expansion | Analysis | Mathematics, general | 11Y60 | Eulerian fraction | Applications of Mathematics | 26D15 | Inequality | MATHEMATICS | MATHEMATICS, APPLIED | SERIES | ASYMPTOTIC EXPANSIONS | CONVERGENT | PSI FUNCTION | Somos' quadratic recurrence constant | DOUBLE INTEGRALS | Thermal expansion | Asymptotic series

Journal Article

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, 10/2013, Volume 469, Issue 2158, pp. 20130231 - 20130231

We present a new method for electronic structure calculations based on novel algorithms for nonlinear approximations. We maintain a functional form for the...

Nonlinear approximations | Electronic structure | Hartree-Fock equations | Multi-resolution methods | Numerical calculus | MULTIDISCIPLINARY SCIENCES | nonlinear approximations | ALGORITHMS | HARTREE-FOCK | DENSITY | multi-resolution methods | MULTIRESOLUTION QUANTUM-CHEMISTRY | QUADRATIC WAVE FUNCTIONS | MULTIWAVELET BASES | electronic structure | numerical calculus | MOLECULAR PROBLEMS | GROUND-STATES | Orbitals | Algorithms | Approximation | Mathematical analysis | Nonlinearity | Mathematical models | Representations

Nonlinear approximations | Electronic structure | Hartree-Fock equations | Multi-resolution methods | Numerical calculus | MULTIDISCIPLINARY SCIENCES | nonlinear approximations | ALGORITHMS | HARTREE-FOCK | DENSITY | multi-resolution methods | MULTIRESOLUTION QUANTUM-CHEMISTRY | QUADRATIC WAVE FUNCTIONS | MULTIWAVELET BASES | electronic structure | numerical calculus | MOLECULAR PROBLEMS | GROUND-STATES | Orbitals | Algorithms | Approximation | Mathematical analysis | Nonlinearity | Mathematical models | Representations

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 10/2018, Volume 340, pp. 602 - 614

The efficient numerical integration of large-scale matrix differential equations is a topical problem in numerical analysis and of great importance in many...

Dynamical low-rank approximation | Differential Lyapunov equations | Linear quadratic regulator problem | Splitting integrators | El Niño simulation | Differential Riccati equations | MATHEMATICS, APPLIED | El Nino simulation | Weather | Numerical analysis | Analysis | Differential equations

Dynamical low-rank approximation | Differential Lyapunov equations | Linear quadratic regulator problem | Splitting integrators | El Niño simulation | Differential Riccati equations | MATHEMATICS, APPLIED | El Nino simulation | Weather | Numerical analysis | Analysis | Differential equations

Journal Article