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Applied numerical analysis using MATLAB / Laurene V. Fausett.

By: Fausett, Laurene V.
Material type: materialTypeLabelBookPublisher: Upper Saddle River, NJ : Pearson Prentice Hall, 2008Edition: 2nd edition.Description: xiii, 673 p. : ill. ; 25 cm.ISBN: 9780132397285; 0132397285.Subject(s): MATLAB | Numerical analysis -- Data processingDDC classification: 518
Contents:
Foundations -- Functions of one variable -- Solving linear systems: direct methods -- Lu and qr factorization -- Eigenvalues and eigenvectors -- Solving linear systems: iterative methods -- Nonlinear functions of several variables -- Interpolation -- Approximation -- Fourier methods -- Numerical differentiation and integration -- Ordinary differential equations: fundamentals -- ODE: systems, stiffness, stability -- ODE: boundary-value problems -- Partial differential equations.
Holdings
Item type Current library Call number Copy number Status Barcode
General lending MTU Bishopstown Library Lending 518 (Browse shelf(Opens below)) 1 Available 00131358
General lending MTU Bishopstown Library Lending 518 (Browse shelf(Opens below)) 1 Available 00131973
Total holds: 0

Enhanced descriptions from Syndetics:

Uses introductory problems from particular applications that are easy to understand and show the reader that there is a need for a particular mathematical technique. Numerical techniques are explained from basics with an emphasis on why they work. Discusses the contexts and reasons for selection of each problem and solution method. Worked-out examples are very realistic and not contrived.

Bibliography: (pages 643-652) and index.

Foundations -- Functions of one variable -- Solving linear systems: direct methods -- Lu and qr factorization -- Eigenvalues and eigenvectors -- Solving linear systems: iterative methods -- Nonlinear functions of several variables -- Interpolation -- Approximation -- Fourier methods -- Numerical differentiation and integration -- Ordinary differential equations: fundamentals -- ODE: systems, stiffness, stability -- ODE: boundary-value problems -- Partial differential equations.

CIT Module MATH 7016 - Core reading

Table of contents provided by Syndetics

  • Preface (p. xi)
  • 1 Foundations (p. 1)
  • 1.1 Introductory Examples (p. 4)
  • 1.1.1 Nonlinear Equations (p. 4)
  • 1.1.2 Linear Systems (p. 6)
  • 1.1.3 Numerical Integration (p. 8)
  • 1.2 Useful Background (p. 10)
  • 1.2.1 Results from Calculus (p. 10)
  • 1.2.2 Results from Linear Algebra (p. 11)
  • 1.2.3 A Little Information about Computers (p. 13)
  • 1.3 Some Basic Issues (p. 16)
  • 1.3.1 Error (p. 16)
  • 1.3.2 Convergence (p. 22)
  • 1.3.3 Getting Better Results (p. 26)
  • 1.4 Using MATLAB (p. 31)
  • 1.4.1 Command Window Computations (p. 31)
  • 1.4.2 M-Files (p. 35)
  • 1.4.3 Programming in MATLAB (p. 37)
  • 1.4.4 Matrix Multiplication (p. 39)
  • 1.5 Chapter Wrap-Up (p. 41)
  • 2 Functions of One Variable (p. 47)
  • 2.1 Bisection Method (p. 50)
  • 2.2 Secant-Type Methods (p. 54)
  • 2.2.1 Regula Falsi (p. 55)
  • 2.2.2 Secant Method (p. 58)
  • 2.2.3 Analysis (p. 61)
  • 2.3 Newton's Method (p. 64)
  • 2.4 Muller's Method (p. 71)
  • 2.5 Minimization (p. 76)
  • 2.5.1 Golden-Section Search (p. 76)
  • 2.5.2 Brent's Method (p. 79)
  • 2.6 Beyond the Basics (p. 80)
  • 2.6.1 Using MATLAB's Functions (p. 80)
  • 2.6.2 Laguerre's Method (p. 82)
  • 2.6.3 Zeros of a Nonlinear Function (p. 85)
  • 2.7 Chapter Wrap-Up (p. 88)
  • 3 Solving Linear Systems: Direct Methods (p. 95)
  • 3.1 Gaussian Elimination (p. 98)
  • 3.1.1 Basic Method (p. 98)
  • 3.1.2 Row Pivoting (p. 107)
  • 3.2 Gauss-Jordan (p. 112)
  • 3.2.1 Inverse of a Matrix (p. 113)
  • 3.3 Tridiagonal Systems (p. 114)
  • 3.4 Further Topics (p. 119)
  • 3.4.1 MATLAB's Methods (p. 119)
  • 3.4.2 Condition of a Matrix (p. 121)
  • 3.4.3 Iterative Refinement (p. 123)
  • 3.5 Chapter Wrap-Up (p. 125)
  • 4 LU and QR Factorization (p. 135)
  • 4.1 LU Factorization (p. 138)
  • 4.1.1 Using Gaussian Elimination (p. 138)
  • 4.1.2 Direct LU Factorization (p. 146)
  • 4.1.3 Applications (p. 150)
  • 4.2 Matrix Transformations (p. 154)
  • 4.2.1 Householder Transformation (p. 155)
  • 4.2.2 Givens Rotations (p. 162)
  • 4.3 QR Factorization (p. 164)
  • 4.3.1 Using Householder Transformations (p. 164)
  • 4.3.2 Using Givens Rotations (p. 166)
  • 4.4 Beyond the Basics (p. 168)
  • 4.4.1 LU Factorization with Implicit Row Pivoting (p. 168)
  • 4.4.2 Efficient Conversion to Hessenberg Form (p. 170)
  • 4.4.3 Using MATLAB's Functions (p. 171)
  • 4.5 Chapter Wrap-Up (p. 172)
  • 5 Eigenvalues and Eigenvectors (p. 179)
  • 5.1 Power Method (p. 182)
  • 5.1.1 Basic Power Method (p. 183)
  • 5.1.2 Rayleigh Quotient (p. 186)
  • 5.1.3 Shifted Power Method (p. 188)
  • 5.1.4 Accelerating Convergence (p. 189)
  • 5.2 Inverse Power Method (p. 190)
  • 5.2.1 General Inverse Power Method (p. 192)
  • 5.2.2 Convergence (p. 193)
  • 5.3 QR Method (p. 194)
  • 5.3.1 Basic QR Method (p. 194)
  • 5.3.2 Better QR Method (p. 196)
  • 5.3.3 Finding Eigenvectors (p. 198)
  • 5.3.4 Accelerating Convergence (p. 199)
  • 5.4 Further Topics (p. 202)
  • 5.4.1 Singular Value Decomposition (p. 202)
  • 5.4.2 MATLAB's Methods (p. 203)
  • 5.5 Chapter Wrap-Up (p. 204)
  • 6 Solving Linear Systems: Iterative Methods (p. 213)
  • 6.1 Jacobi Method (p. 217)
  • 6.2 Gauss-Seidel Method (p. 224)
  • 6.3 Successive Over-Relaxation (p. 228)
  • 6.4 Beyond the Basics (p. 232)
  • 6.4.1 MATLAB's Built-in Functions (p. 232)
  • 6.4.2 Conjugate Gradient Methods (p. 234)
  • 6.4.3 GMRES (p. 238)
  • 6.4.4 Simplex Method (p. 240)
  • 6.5 Chapter Wrap-Up (p. 243)
  • 7 Nonlinear Functions of Several Variables (p. 251)
  • 7.1 Nonlinear Systems (p. 254)
  • 7.1.1 Newton's Method (p. 254)
  • 7.1.2 Secant Methods (p. 260)
  • 7.1.3 Fixed-Point Iteration (p. 262)
  • 7.2 Minimization (p. 264)
  • 7.2.1 Descent Methods (p. 264)
  • 7.2.2 Quasi-Newton Methods (p. 266)
  • 7.3 Further Topics (p. 268)
  • 7.3.1 Levenberg-Marquardt Method (p. 268)
  • 7.3.2 Nelder-Mead Simplex Search (p. 269)
  • 7.4 Chapter Wrap-Up (p. 270)
  • 8 Interpolation (p. 275)
  • 8.1 Polynomial Interpolation (p. 278)
  • 8.1.1 Lagrange Form (p. 278)
  • 8.1.2 Newton Form (p. 284)
  • 8.1.3 Difficulties (p. 290)
  • 8.2 Hermite Interpolation (p. 294)
  • 8.3 Piecewise Polynomial Interpolation (p. 299)
  • 8.3.1 Piecewise Linear Interpolation (p. 300)
  • 8.3.2 Piecewise Quadratic Interpolation (p. 301)
  • 8.3.3 Piecewise Cubic Hermite Interpolation (p. 304)
  • 8.3.4 Cubic Spline Interpolation (p. 305)
  • 8.4 Beyond the Basics (p. 312)
  • 8.4.1 Rational-Function Interpolation (p. 312)
  • 8.4.2 Using MATLAB's Functions (p. 316)
  • 8.5 Chapter Wrap-Up (p. 323)
  • 9 Approximation (p. 333)
  • 9.1 Least-Squares Approximation (p. 336)
  • 9.1.1 Approximation by a Straight Line (p. 336)
  • 9.1.2 Approximation by a Parabola (p. 342)
  • 9.1.3 General Least-Squares Approximation (p. 346)
  • 9.1.4 Approximation for Other Functional Forms (p. 348)
  • 9.2 Continuous Least-Squares Approximation (p. 350)
  • 9.2.1 Approximation Using Powers of x (p. 350)
  • 9.2.2 Orthogonal Polynomials (p. 352)
  • 9.2.3 Legendre Polynomials (p. 354)
  • 9.2.4 Chebyshev Polynomials (p. 356)
  • 9.3 Function Approximation at a Point (p. 358)
  • 9.3.1 Pade Approximation (p. 358)
  • 9.3.2 Taylor Approximation (p. 361)
  • 9.4 Further Topics (p. 362)
  • 9.4.1 Bezier Curves (p. 362)
  • 9.4.2 Using MATLAB's Functions (p. 364)
  • 9.5 Chapter Wrap-Up (p. 366)
  • 10 Fourier Methods (p. 373)
  • 10.1 Fourier Approximation and Interpolation (p. 376)
  • 10.1.1 Derivation (p. 381)
  • 10.1.2 Data on Other Intervals (p. 384)
  • 10.2 Radix-2 Fourier Transforms (p. 386)
  • 10.2.1 Discrete Fourier Transform (p. 386)
  • 10.2.2 Fast Fourier Transform (p. 387)
  • 10.2.3 Matrix Form of FFT (p. 388)
  • 10.2.4 Algebraic Form of FFT (p. 389)
  • 10.3 Mixed-Radix FFT (p. 392)
  • 10.4 Using MATLAB's Functions (p. 396)
  • 10.5 Chapter Wrap-Up (p. 400)
  • 11 Numerical Differentiation and Integration (p. 405)
  • 11.1 Differentiation (p. 408)
  • 11.1.1 First Derivatives (p. 408)
  • 11.1.2 Higher Derivatives (p. 412)
  • 11.1.3 Partial Derivatives (p. 413)
  • 11.1.4 Richardson Extrapolation (p. 414)
  • 11.2 Numerical Integration (p. 416)
  • 11.2.1 Trapezoid Rule (p. 417)
  • 11.2.2 Simpson's Rule (p. 420)
  • 11.2.3 Newton-Cotes Open Formulas (p. 426)
  • 11.2.4 Extrapolation Methods (p. 428)
  • 11.3 Quadrature (p. 431)
  • 11.3.1 Gaussian Quadrature (p. 431)
  • 11.3.2 Other Gauss-Type Quadratures (p. 435)
  • 11.4 MATLAB's Methods (p. 437)
  • 11.4.1 Differentiation (p. 437)
  • 11.4.2 Integration (p. 437)
  • 11.5 Chapter Wrap-Up (p. 438)
  • 12 Ordinary Differential Equations: Fundamentals (p. 445)
  • 12.1 Euler's Method (p. 447)
  • 12.1.1 Geometric Introduction (p. 447)
  • 12.1.2 Approximating the Derivative (p. 448)
  • 12.1.3 Approximating the Integral (p. 449)
  • 12.1.4 Using Taylor Series (p. 451)
  • 12.2 Runge-Kutta Methods (p. 452)
  • 12.2.1 Second-Order Runge-Kutta Methods (p. 452)
  • 12.2.2 Third-Order Runge-Kutta Methods (p. 457)
  • 12.2.3 Classic Runge-Kutta Method (p. 459)
  • 12.2.4 Fourth-Order Runge-Kutta Methods (p. 462)
  • 12.2.5 Fifth-Order Runge-Kutta Methods (p. 464)
  • 12.2.6 Runge-Kutta-Fehlberg Methods (p. 465)
  • 12.3 Multistep Methods (p. 474)
  • 12.3.1 Adams-Bashforth Methods (p. 476)
  • 12.3.2 Adams-Moulton Methods (p. 479)
  • 12.3.3 Adams Predictor-Corrector Methods (p. 480)
  • 12.3.4 Other Predictor-Corrector Methods (p. 485)
  • 12.4 Further Topics (p. 487)
  • 12.4.1 MATLAB's Methods (p. 487)
  • 12.4.2 Consistency and Convergence (p. 488)
  • 12.5 Chapter Wrap-Up (p. 490)
  • 13 ODE: Systems, Stiffness, Stability (p. 499)
  • 13.1 Systems (p. 502)
  • 13.1.1 Systems of Two ODE (p. 504)
  • 13.1.2 Euler's Method for Systems (p. 510)
  • 13.1.3 Runge-Kutta Methods for Systems (p. 512)
  • 13.1.4 Multistep Methods for Systems (p. 516)
  • 13.1.5 Second-Order ODE (p. 522)
  • 13.2 Stiff ODE (p. 526)
  • 13.2.1 BDF Methods (p. 527)
  • 13.2.2 Implicit Runge-Kutta Methods (p. 529)
  • 13.3 Stability (p. 530)
  • 13.3.1 A-Stable and Stiffly Stable Methods (p. 532)
  • 13.3.2 Stability in the Limit (p. 533)
  • 13.4 Further Topics (p. 536)
  • 13.4.1 MATLAB's Methods for Stiff ODE (p. 536)
  • 13.4.2 Extrapolation Methods (p. 537)
  • 13.4.3 Rosenbrock Methods (p. 539)
  • 13.4.4 Multivalue Methods (p. 539)
  • 13.5 Chapter Wrap-Up (p. 552)
  • 14 ODE: Boundary-Value Problems (p. 561)
  • 14.1 Shooting Method (p. 565)
  • 14.1.1 Linear ODE (p. 565)
  • 14.1.2 Nonlinear ODE (p. 570)
  • 14.2 Finite-Difference Method (p. 576)
  • 14.2.1 Linear ODE (p. 576)
  • 14.2.2 Nonlinear ODE (p. 580)
  • 14.3 Function Space Methods (p. 582)
  • 14.3.1 Collocation (p. 582)
  • 14.3.2 Rayleigh-Ritz (p. 586)
  • 14.4 Chapter Wrap-Up (p. 588)
  • 15 Partial Differential Equations (p. 593)
  • 15.1 Heat Equation: Parabolic PDE (p. 598)
  • 15.1.1 Explicit Method (p. 599)
  • 15.1.2 Implicit Method (p. 604)
  • 15.1.3 Crank-Nicolson Method (p. 608)
  • 15.1.4 Insulated Boundary (p. 611)
  • 15.2 Wave Equation: Hyperbolic PDE (p. 612)
  • 15.2.1 Explicit Method (p. 614)
  • 15.2.2 Implicit Method (p. 616)
  • 15.3 Poisson Equation: Elliptic PDE (p. 618)
  • 15.4 Finite-Element Method for Elliptic PDE (p. 622)
  • 15.4.1 Defining the Subregions (p. 623)
  • 15.4.2 Defining the Basis Functions (p. 624)
  • 15.4.3 Computing the Coefficients (p. 626)
  • 15.4.4 Using MATLAB (p. 629)
  • 15.5 Chapter Wrap-Up (p. 634)
  • Bibliography (p. 643)
  • Answers (p. 653)
  • Index (p. 667)