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2540 results in Computational Science

Page 39 of 127

Data-Driven Computational Methods
  • Parameter and Operator Estimations
  • John Harlim
  • Published online:
    06 July 2018
    Print publication:
    12 July 2018
  • Modern scientific computational methods are undergoing a transformative change; big data and statistical learning methods now have the potential to outperform the classical first-principles modeling paradigm. This book bridges this transition, connecting the theory of probability, stochastic processes, functional analysis, numerical analysis, and differential geometry. It describes two classes of computational methods to leverage data for modeling dynamical systems. The first is concerned with data fitting algorithms to estimate parameters in parametric models that are postulated on the basis of physical or dynamical laws. The second is on operator estimation, which uses the data to nonparametrically approximate the operator generated by the transition function of the underlying dynamical systems. This self-contained book is suitable for graduate studies in applied mathematics, statistics, and engineering. Carefully chosen elementary examples with supplementary MATLAB® codes and appendices covering the relevant prerequisite materials are provided, making it suitable for self-study.

Multivariate Approximation
  • V. Temlyakov
  • Published online:
    06 July 2018
    Print publication:
    19 July 2018
  • This self-contained, systematic treatment of multivariate approximation begins with classical linear approximation, and moves on to contemporary nonlinear approximation. It covers substantial new developments in the linear approximation theory of classes with mixed smoothness, and shows how it is directly related to deep problems in other areas of mathematics. For example, numerical integration of these classes is closely related to discrepancy theory and to nonlinear approximation with respect to special redundant dictionaries, and estimates of the entropy numbers of classes with mixed smoothness are closely related to (in some cases equivalent to) the Small Ball Problem from probability theory. The useful background material included in the book makes it accessible to graduate students. Researchers will find that the many open problems in the theory outlined in the book provide helpful directions and guidance for their own research in this exciting and active area.

A Guide to MATLAB®
  • For Beginners and Experienced Users
  • 3rd edition
  • Brian R. Hunt, Ronald L. Lipsman, Jonathan M. Rosenberg
  • Published online:
    28 May 2018
    Print publication:
    21 August 2014
  • Now in its third edition, this outstanding textbook explains everything you need to get started using MATLAB®. It contains concise explanations of essential MATLAB commands, as well as easily understood instructions for using MATLAB's programming features, graphical capabilities, simulation models, and rich desktop interface. MATLAB 8 and its new user interface is treated extensively in the book. New features in this edition include: a complete treatment of MATLAB's publish feature; new material on MATLAB graphics, enabling the user to master quickly the various symbolic and numerical plotting routines; and a robust presentation of MuPAD® and how to use it as a stand-alone platform. The authors have also updated the text throughout, reworking examples and exploring new applications. The book is essential reading for beginners, occasional users and experienced users wishing to brush up their skills. Further resources are available from the authors' website at www-math.umd.edu/schol/a-guide-to-matlab.html.

  • On the zeros of Dirichlet $L$ -functions – RETRACTION

  • Sami Omar, Raouf Ouni, Kamel Mazhouda
  • Journal:
    LMS Journal of Computation and Mathematics / Volume 20 / Issue 1 / 2017
    Published online by Cambridge University Press:
    10 May 2018, p. 53
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  • On the zeros of Dirichlet $L$ -functions

  • Part of
  • Sami Omar, Raouf Ouni, Kamel Mazhouda
  • Journal:
    LMS Journal of Computation and Mathematics / Volume 14 / 2011
    Published online by Cambridge University Press:
    01 May 2018, pp. 140-154
    • Article
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  • This paper [1], which was published online on 1 June 2011, has been retracted by agreement between the authors, the journal’s Editor-in-Chief Derek Holt, the London Mathematical Society and Cambridge University Press. The retraction was agreed to prevent other authors from using incorrect mathematical results. (In this paper, we compute and verify the positivity of the Li coefficients for the Dirichlet $L$ -functions using an arithmetic formula established in Omar and Mazhouda, J. Number Theory 125 (2007) no. 1, 50–58; J. Number Theory 130 (2010) no. 4, 1109–1114. Furthermore, we formulate a criterion for the partial Riemann hypothesis and we provide some numerical evidence for it using new formulas for the Li coefficients.)

Page 39 of 127