David Gottlieb

Bio: David Gottlieb is an academic researcher from Brown University. The author has contributed to research in topics: Boundary value problem & Spectral method. The author has an hindex of 45, co-authored 126 publications receiving 14161 citations. Previous affiliations of David Gottlieb include Langley Research Center & New York University.

Numerical analysis of spectral methods : theory and applications

Abstract: Spectral Methods Survey of Approximation Theory Review of Convergence Theory Algebraic Stability Spectral Methods Using Fourier Series Applications of Algebraic Stability Analysis Constant Coefficient Hyperbolic Equations Time Differencing Efficient Implementation of Spectral Methods Numerical Results for Hyperbolic Problems Advection-Diffusion Equation Models of Incompressible Fluid Dynamics Miscellaneous Applications of Spectral Methods Survey of Spectral Methods and Applications Properties of Chebyshev and Legendre Polynomial Expansions.

Cbms-nsf regional conference series in applied mathematics

Abstract: Spectral Methods in Fluid DynamicsNumerical Methods for Partial Differential EquationsNumerical Analysis of Partial Differential EquationsNumerical analysis of spectral methods : theory and applicationsSpectral Methods And Their ApplicationsA Brief Introduction to Numerical AnalysisA First Course in the Numerical Analysis of Differential Equations South Asian EditionConvergence of Spectral Methods for Hyperbolic Initial-boundary Value SystemsReview of Some Approximation Operators for the Numerical Analysis of Spectral MethodsSpectral Methods in MATLABA Modified Spectral Method in Phase SpaceThe Birth of Numerical AnalysisSpectral Methods for Non-Standard Eigenvalue ProblemsPartial Differential EquationsNumerical Analysis of Spectral MethodsNumerical Analysis of Partial Differential Equations Using Maple and MATLABSpectral MethodsSpectral Methods for NonStandard Eigenvalue ProblemsAn Introduction to the Numerical Analysis of Spectral MethodsSpectral Methods in Time for Parabolic ProblemsSpectral Methods in Chemistry and PhysicsA First Course in the Numerical Analysis of Differential Equations South Asian EditionSummary of Research in Applied Mathematics, Numerical Analysis and Computer Science at the Institute for Computer Applications in Science and EngineeringNumerical AnalysisSpectral Methods for Compressible Flow ProblemsA First Course in the Numerical Analysis of Differential EquationsSummary of Research in Applied Mathematics, Numerical Analysis, and Computer SciencesA Theoretical Introduction to Numerical AnalysisNumerical AnalysisRiemann-Hilbert Problems, Their Numerical Solution, and the Computation of Nonlinear Special FunctionsSpectral MethodsSpectral Methods for Uncertainty QuantificationSpectral Methods and Their ApplicationsNumerical Analysis of Spectral Methods: Theory and ApplicatonsSpectral Methods for Incompressible Viscous FlowAdvances in Numerical Analysis: Nonlinear partial differential equations and dynamical systemsSpectral Methods Using Multivariate Polynomials on the Unit BallA First Course in the Numerical Analysis of Differential EquationsFundamentals of Engineering Numerical AnalysisSpectral Methods for Time-Dependent Problems

Numerical analysis of spectral methods

Abstract: : This monograph gives a mathematical analysis of spectral methods for mixed initial-boundary value problems. Spectral methods have become increasingly popular in recent years, especially since the development of fast transform methods, with applications in numerical weather prediction, numerical simulations of turbulent flows, and other problems where high accuracy is desired for complicated solutions. The development of a mathematical theory is given that explains why spectral methods work and how well they work.

On the Gibbs Phenomenon and Its Resolution

Abstract: The nonuniform convergence of the Fourier series for discontinuous functions, and in particular the oscillatory behavior of the finite sum, was already analyzed by Wilbraham in 1848. This was later named the Gibbs phenomenon. This article is a review of the Gibbs phenomenon from a different perspective. The Gibbs phenomenon, as we view it, deals with the issue of recovering point values of a function from its expansion coefficients. Alternatively it can be viewed as the possibility of the recovery of local information from global information. The main theme here is not the structure of the Gibbs oscillations but the understanding and resolution of the phenomenon in a general setting. The purpose of this article is to review the Gibbs phenomenon and to show that the knowledge of the expansion coefficients is sufficient for obtaining the point values of a piecewise smooth function, with the same order of accuracy as in the smooth case. This is done by using the finite expansion series to construct a different, rapidly convergent, approximation.

A tutorial on support vector regression

Abstract: In this tutorial we give an overview of the basic ideas underlying Support Vector (SV) machines for function estimation. Furthermore, we include a summary of currently used algorithms for training SV machines, covering both the quadratic (or convex) programming part and advanced methods for dealing with large datasets. Finally, we mention some modifications and extensions that have been applied to the standard SV algorithm, and discuss the aspect of regularization from a SV perspective.

Information Theory, Inference and Learning Algorithms

Abstract: Fun and exciting textbook on the mathematics underpinning the most dynamic areas of modern science and engineering.

Finite Volume Methods for Hyperbolic Problems

Abstract: Preface 1. Introduction 2. Conservation laws and differential equations 3. Characteristics and Riemann problems for linear hyperbolic equations 4. Finite-volume methods 5. Introduction to the CLAWPACK software 6. High resolution methods 7. Boundary conditions and ghost cells 8. Convergence, accuracy, and stability 9. Variable-coefficient linear equations 10. Other approaches to high resolution 11. Nonlinear scalar conservation laws 12. Finite-volume methods for nonlinear scalar conservation laws 13. Nonlinear systems of conservation laws 14. Gas dynamics and the Euler equations 15. Finite-volume methods for nonlinear systems 16. Some nonclassical hyperbolic problems 17. Source terms and balance laws 18. Multidimensional hyperbolic problems 19. Multidimensional numerical methods 20. Multidimensional scalar equations 21. Multidimensional systems 22. Elastic waves 23. Finite-volume methods on quadrilateral grids Bibliography Index.