Books from SIAM

  • Ordinary Differential Equations and Linear Algebra: A Systems Approach
    Ordinary Differential Equations and Linear Algebra: A Systems Approach
    By Todd Kapitula

    ... for in this case [yp](s)=s[yp](s), [yp](s)=s2[yp](s). As we will see in the examples, this assumption also makes it possible to deal with the initial ...

  • A Multigrid Tutorial: Second Edition
    A Multigrid Tutorial: Second Edition
    By William L. Briggs, Van Emden Henson, Steve F. McCormick

    The spectral radius is considered to be an asymptotic measure of convergence because it predicts the worst-case error reduction over many iterations. It can be shown [9, 20] that, in any vector norm, p(R) : llRmlll/mTherefore, ...

  • The DFT: An Owners' Manual for the Discrete Fourier Transform
    The DFT: An Owners' Manual for the Discrete Fourier Transform
    By William L. Briggs, Van Emden Henson

    First, the matrix factorization idea can be applied directly to the radix-r case (see problem 245). A greater challenge is to extend it to the mixed-radix case in which N is a product of powers of different integers; but it can be done.

  • An Introduction to Inverse Scattering and Inverse Spectral Problems
    An Introduction to Inverse Scattering and Inverse Spectral Problems
    By Khosrow Chadan, David Colton, William Rundell

    We should notice here that φ1(iγ, r) ∼ e2γr as r → ∞. This, when used in (4.23) and (4.21), shows that φ(iγ, r) ∼e−γr, as expected. The next simple case is described in §4.4.3. 4.4.3. Phase-Equivalent Potentials.

  • Riemann-Hilbert Problems, Their Numerical Solution, and the Computation of Nonlinear Special Functions
    Riemann-Hilbert Problems, Their Numerical Solution, and the Computation of Nonlinear Special Functions
    By Thomas Trogdon, Sheehan Olver

    Many problems in differential equations and integrable systems, probability and random matrix theory, and asymptotic analysis can be solved by reformulation as a Riemann?Hilbert problem.This book, the most comprehensive one to date on the ...

  • Axiomatic Consensus Theory in Group Choice and Biomathematics
    Axiomatic Consensus Theory in Group Choice and Biomathematics
    By William H. E. Day, F. R. McMorris

    6 T. Flanagan [169, p. 394] The quotation appears to suggest that the retrieval of information from human memory ... Always |H| > n since S G H and {x} G H for all x G S. Moreover for all X, Y G H only three possibilities exist: X g Y, ...

  • Classical Control Using H-Infinity Methods: An Introduction to Design
    Classical Control Using H-Infinity Methods: An Introduction to Design
    By J. William Helton, Orlando Merino

    However, the optimization routine Anopt used by OPTDesign has capability of solving many optimization problems of a kind that ... Thanks Thanks to Trent Walker, David Ring, Robert O'Barr, David Schwartz, Neola Crimmins, Joy Kirsch, ...

  • The DFT: An Owners' Manual for the Discrete Fourier Transform
    The DFT: An Owners' Manual for the Discrete Fourier Transform
    By William L. Briggs, Van Emden Henson

    [162] E. WHITTAKER AND G. ROBINSON, The Calculus of Observation, Blackie and Sons, London, 1924. [163] O. WING, An efficient method of numerical inversion of Laplace transforms, Arch. Elect. Comp., 2 (1967), p. 153.

  • Numerically Solving Polynomial Systems with Bertini
    Numerically Solving Polynomial Systems with Bertini
    By Daniel J. Bates, Jonathan D. Hauenstein, Andrew J. Sommese

    This book is a guide to concepts and practice in numerical algebraic geometry ? the solution of systems of polynomial equations by numerical methods.

  • Mathematical Models in Biology
    Mathematical Models in Biology
    By Leah Edelstein-Keshet

    Ross, S. L. (1984). Differential Equations. 3d ed. Wiley, New York, chap. 13. 6 Applications of Continuous Models to Population Dynamics Each organic Phase-Plane Methods and Qualitative Solutions 209.

  • Foundations of Applied Mathematics, Volume I: Mathematical Analysis
    Foundations of Applied Mathematics, Volume I: Mathematical Analysis
    By Jeffrey Humpherys, Tyler J. Jarvis, Emily J. Evans

    [624] John Hamal Hubbard and Barbara Burke Hubbard. Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach. Prentice– Hall, Upper Saddle River, NJ, 1999. [406] Jeffrey Humpherys, Preston Redd, and Jeremy West.

  • Minimum-volume Ellipsoids: Theory and Algorithms
    Minimum-volume Ellipsoids: Theory and Algorithms
    By Michael J. Todd

    Since ZUZ" is singular, there is a nonzero w with ZUZ" w = 0, and then * 7T-., - A T-. 4 - ~7 - – 4 (..T 0% ZUZ'w =(1-t)ZUZ'w-à,2,2; w = \,(z; w)2, so that z/w is nonzero. Also, w” ZUZ" w = 0, whence U"Z" w = 0, and so YUZZ w = 0.

  • Ordinary Differential Equations and Linear Algebra: A Systems Approach
    Ordinary Differential Equations and Linear Algebra: A Systems Approach
    By Todd Kapitula

    Ordinary differential equations (ODEs) and linear algebra are foundational postcalculus mathematics courses in the sciences. The goal of this text is to help students master both subject areas in a one-semester course.

  • Matrix Analysis for Scientists and Engineers
    Matrix Analysis for Scientists and Engineers
    By Alan J. Laub

    In this chapter we give a brief introduction to the Moore–Penrose pseudoinverse, a generalization of the inverse of a matrix. The Moore–Penrose pseudoinverse is defined for any matrix and, as is shown in the following text, brings great ...

  • Primal-Dual Interior-Point Methods
    Primal-Dual Interior-Point Methods
    By Stephen J. Wright

    [128 M. TODD, Potential reduction methods in mathematical programming, Technical Report 1112, Cornell University, Ithaca, N.Y., 1995. To appear in Mathematical Programming, Series B. |129) M. ToDD AND B. P. BURRELL, An extension of ...

  • Optimization Software Guide
    Optimization Software Guide
    By Stephen J. Wright, Jorge J. Moré

    [17] P. E. Gill, W. Murray, M. A. Saunders, and M. H. Wright, Constrained nonlinear programming, in Optimization, G. L. Nemhauser, A. H. G. Rinnooy Kan, and M. J. Todd, eds., North—Holland, Amsterdam, 1989, pp. 171—210.

  • Introduction to High Performance Scientific Computing
    Introduction to High Performance Scientific Computing
    By David L. Chopp

    156) R. COURANT, K. FRIEDRICHS, AND H. LEWY, Partial Difference Equations of Mathematical Physics, Mathematische Annalen, 100 (1928), pp. 32–74. (Cited on p. 172) J. SANDERS AND E. KANDROT, CUDA By Example, Pearson Education, Inc., ...

  • Numerical Methods for Conservation Laws: From Analysis to Algorithms
    Numerical Methods for Conservation Laws: From Analysis to Algorithms
    By Jan S. Hesthaven

    Pearson Education, 2007. [13] Yongcheng Zhou and Guo-Wei Wei. High resolution conjugate filters for the simulation of flows. Journal of Computational Physics, 189(1):159–179, 2003. Chapter 8 High-order accuracy and its challenges ...

  • Mining Imperfect Data: Dealing with Contamination and Incomplete Records
    Mining Imperfect Data: Dealing with Contamination and Incomplete Records
    By Ronald K. Pearson

    Levitt and Snyder Jr. (1997) considered the problem of estimating the influence of federal fundraising on the outcomes of US. House of Representatives elections. They begin by noting that, although it is widely believed by “academics, ...

  • Functions of a Complex Variable: Theory and Technique
    Functions of a Complex Variable: Theory and Technique
    By George F. Carrier, Max Krook, Carl E. Pearson

    Editor—in'Chief Robert E. O'Malley, Jr., University of Washington Editorial Board John Boyd, University of Michigan Leah Edelstein—Keshet, University of British Columbia William G. Paris, University of Arizona Nicholas J. Higham, ...