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4163 results in Numerical analysis and computational science

Page 42 of 209

  • 1 - Introduction to MATLAB

  • Jaan Kiusalaas, Pennsylvania State University
  • Book:
    Numerical Methods in Engineering with MATLAB®
    Published online:
    28 May 2018
    Print publication:
    20 October 2015, pp 1-26

  • Summary

    Quick Overview

    This chapter is not intended to be a comprehensive manual of MATLAB®. Our sole aim is to provide sufficient information to give you a good start. If you are familiar with another computer language, and we assume that you are, it is not difficult to pick up the rest as you go.

    MATLAB is a high-level computer language for scientific computing and data visualization built around an interactive programming environment. It is becoming the premiere platform for scientific computing at educational institutions and research establishments. The great advantage of an interactive system is that programs can be tested and debugged quickly, allowing the user to concentrate more on the principles behind the program and less on programming itself. Because there is no need to compile, link, and execute after each correction, MATLAB programs can be developed in a much shorter time than equivalent FORTRAN or C programs. On the negative side, MATLAB does not produce stand-alone applications – the programs can be run only on computers that have MATLAB installed.

    MATLAB has other advantages over mainstream languages that contribute to rapid program development:

  • • MATLAB contains a large number of functions that access proven numerical libraries, such as LINPACK and EISPACK. This means that many common tasks (e.g., solution of simultaneous equations) can be accomplished with a single function call.

  • • Extensive graphics support allows the results of computations to be plotted with a few statements.

  • • All numerical objects are treated as double-precision arrays. Thus there is no need to declare data types and carry out type conversions.

  • • MATLAB programs are clean and easy to read; they lack the syntactic clutter of some mainstream languages (e.g., C).

    • The syntax of MATLAB resembles that of FORTRAN. To get an idea of the similarities between these programming languages, let us compare the codes written in the two languages for solution of simultaneous equations Ax = b by Gauss elimination (do not worry about understanding the inner workings of the programs).

Numerical Methods in Engineering with MATLAB®
  • 3rd edition
  • Jaan Kiusalaas
  • Published online:
    28 May 2018
    Print publication:
    20 October 2015
  • The third edition of this successful text describes and evaluates a range of widely used numerical methods, with an emphasis on problem solving. Every method is discussed thoroughly and illustrated with problems involving both hand computation and programming. MATLAB® M-files accompany each method and are available on the book's web page. Code is made simple and easy to understand by avoiding complex book-keeping schemes, while maintaining the essential features of the method. The third edition features a new chapter on Euler's method, a number of new and improved examples and exercises, and programs which appear as function M-files. Numerical Methods in Engineering with MATLAB®, 3rd edition is a useful resource for both graduate students and practicing engineers.

  • THE RELEVANT FRAGMENT OF FIRST ORDER LOGIC

  • GUILLERMO BADIA
  • Journal:
    The Review of Symbolic Logic / Volume 9 / Issue 1 / March 2016
    Published online by Cambridge University Press:
    20 October 2015, pp. 143-166
    Print publication:
    March 2016

  • Under a proper translation, the languages of propositional (and quantified relevant logic) with an absurdity constant are characterized as the fragments of first order logic preserved under (world-object) relevant directed bisimulations. Furthermore, the properties of pointed models axiomatizable by sets of propositional relevant formulas have a purely algebraic characterization. Finally, a form of the interpolation property holds for the relevant fragment of first order logic.

  • INDICATIVE CONDITIONALS, RESTRICTED QUANTIFICATION, AND NAIVE TRUTH

  • HARTRY FIELD
  • Journal:
    The Review of Symbolic Logic / Volume 9 / Issue 1 / March 2016
    Published online by Cambridge University Press:
    19 October 2015, pp. 181-208
    Print publication:
    March 2016

  • This paper extends Kripke’s theory of truth to a language with a variably strict conditional operator, of the kind that Stalnaker and others have used to represent ordinary indicative conditionals of English. It then shows how to combine this with a different and independently motivated conditional operator, to get a substantial logic of restricted quantification within naive truth theory.

  • Mordell’s equation: a classical approach

  • Part of
  • Michael A. Bennett, Amir Ghadermarzi
  • Journal:
    LMS Journal of Computation and Mathematics / Volume 18 / Issue 1 / 2015
    Published online by Cambridge University Press:
    01 September 2015, pp. 633-646
    • Article
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  • We solve the Diophantine equation $Y^{2}=X^{3}+k$ for all nonzero integers $k$ with $|k|\leqslant 10^{7}$. Our approach uses a classical connection between these equations and cubic Thue equations. The latter can be treated algorithmically via lower bounds for linear forms in logarithms in conjunction with lattice-basis reduction.

  • A quasi-linear time algorithm for computing modular polynomials in dimension 2

  • Part of
  • Enea Milio
  • Journal:
    LMS Journal of Computation and Mathematics / Volume 18 / Issue 1 / 2015
    Published online by Cambridge University Press:
    01 September 2015, pp. 603-632
    • Article
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  • We propose to generalize the work of Régis Dupont for computing modular polynomials in dimension $2$ to new invariants. We describe an algorithm to compute modular polynomials for invariants derived from theta constants and prove heuristically that this algorithm is quasi-linear in its output size. Some properties of the modular polynomials defined from quotients of theta constants are analyzed. We report on experiments with our implementation.

  • REFLEXIVE-INSENSITIVE MODAL LOGICS

  • DAVID R. GILBERT, GIORGIO VENTURI
  • Journal:
    The Review of Symbolic Logic / Volume 9 / Issue 1 / March 2016
    Published online by Cambridge University Press:
    24 August 2015, pp. 167-180
    Print publication:
    March 2016

  • We analyze a class of modal logics rendered insensitive to reflexivity by way of a modification to the semantic definition of the modal operator. We explore the extent to which these logics can be characterized, and prove a general completeness theorem on the basis of a translation between normal modal logics and their reflexive-insensitive counterparts. Lastly, we provide a sufficient semantic condition describing when a similarly general soundness result is also available.

  • RSL volume 8 issue 3 Cover and Front matter

  • Journal:
    The Review of Symbolic Logic / Volume 8 / Issue 3 / September 2015
    Published online by Cambridge University Press:
    24 August 2015, pp. f1-f4
    Print publication:
    September 2015
    • Article
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Page 42 of 209