부산대학교 도서관

국외단행본

Introduction to numerical analysis using MATLAB / Rizwan Butt.

Sudbury, Mass. : Jones and Bartlett Publishers , c2010.

xv, 814 p. : ill. ; 25 cm. + 1 CD-ROM (4 3/4 in.)

Includes bibliographical references (p. 801-808) and index.

1. Number systems and errors -- 1.1. Introduction -- 1.2. Number representation and base of numbers -- 1.2.1. Normalized floating-point representation -- 1.2.2. Rounding and chopping -- 1.3. Error -- 1.4. Sources of errors -- 1.4.1. Human error -- 1.4.2. Truncation error -- 1.4.3. Round-off error -- 1.5. Effect of round-off errors in arithmetic operations -- 1.5.1. Rounding-off errors in addition and subtraction -- 1.5.2. Rounding-off errors in multiplication -- 1.5.3. Rounding-off errors in division -- 1.5.4. Rounding-off errors in powers and roots -- 1.6. Summary -- 1.7. Exercises -- 2. Solutions of nonlinear equations -- 2.1. Introduction -- 2.2. Method of bisection -- 2.3. False position method -- 2.4. Fixed-point method -- 2.5. Newton's method -- 2.6. Secant method -- 2.7. Multiplicity of a root -- 2.8. Convergence of iterative methods -- 2.9. Acceleration of convergence -- 2.10. Systems of nonlinear equations 85 -- 2.10.1. Newton's method -- 2.11. Roots of polynomials -- 2.11.1. Horner's method -- 2.11.2. Muller's method -- 2.11.3. Bairstow's method -- 2.12. Summary -- 2.13. Exercises --
3. Systems of linear equations -- 3.1. Introduction -- 3.1.1. Linear system in matrix notation -- 3.2. Properties of matrices and determinants -- 3.2.1. Introduction of matrices -- 3.2.2. Some special matrix forms -- 3.2.3. The determinant of matrix -- 3.3. Numerical methods for linear systems -- 3.4. Direct methods for linear systems -- 3.4.1. Cramer's rule -- 3.4.2. Gaussian elimination method -- 3.4.3. Pivoting strategies -- 3.4.4. Gauss-Jordan method -- 3.4.5. LU decomposition method -- 3.4.6. Tridiagonal systems of linear equations -- 3.5. Norms of vectors and matrices -- 3.5.1. Vector norms -- 3.5.2. Matrix norms -- 3.6. Iterative methods for solving linear systems -- 3.6.1. Jacobi iterative method -- 3.6.2. Gauss-Seidel iterative method -- 3.6.3. Convergence criteria -- 3.7. Eigenvalues and eigenvectors -- 3.7.1. Successive over-relaxation method -- 3.7.2. Conjugate gradient method -- 3.8. Conditioning of linear systems -- 3.8.1. Errors in solving linear systems -- 3.8.2. Iterative refinement -- 3.9. Summary -- 3.10. Exercises --
4. Approximating functions -- 4.1. Introduction -- 4.2. Polynomial interpolation for uneven intervals -- 4.2.1. Language interpolating polynomials -- 4.2.2. Newton's general interpolating formula -- 4.2.3. Aitken's method -- 4.3. Polynomial interpolation for even intervals -- 4.3.1. Forward-differences -- 4.3.2. Backward-differences -- 4.3.3. Central-differences -- 4.4. Interpolation with spline functions -- 4.4.1. Natural cubic spline -- 4.4.2. Clamped spline -- 4.5. Least squares approximation -- 4.5.1. Linear least squares -- 4.5.2. Polynomial least squares -- 4.5.3. Nonlinear least squares -- 4.5.4. Least squares plane -- 4.5.5. Overdetermined linear systems -- 4.5.6. Least squares with QR decomposition -- 4.5.7. Least squares with singular value decomposition -- 4.6. Summary -- 4.7. Exercises -- 5. Differentiation and integration -- 5.1. Introduction -- 5.2. Numerical differentiation -- 5.3. Numerical differentiation formulas -- 5.3.1. First derivatives formulas -- 5.3.2. Second derivatives formulas -- 5.4. Formulas for computing derivatives -- 5.4.1. Central difference formulas -- 5.4.2. Forward- and backward-difference formulas -- 5.5. Numerical integration -- 5.6. Newton-Cotes formulas -- 5.6.1. Closed Newton-Cotes formulas-- 5.6.2. Open Newton-Cotes formulas -- 5.7. Repeated use of the trapezoidal rule -- 5.8. Romberg integration -- 5.9. Gaussian quadratures -- 5.10. Summary -- 5.11. Exercises --
6. Ordinary differential equations -- 6.1. Introduction -- 6.1.1. Classification of differential equations -- 6.2. Numerical methods for solving IVP -- 6.3. Single-step methods for IVP -- 6.3.1. Euler's method -- 6.3.2. Analysis of Euler's methods -- 6.3.3. Higher-order Taylor methods -- 6.3.4. Runge-Kutta methods -- 6.3.5. Third-order Ringa-Kutta method -- 6.3.6. Fourth-order Runge-Kutta method -- 6.3.7. Fifth-order Runge-Kutta method -- 6.3.8. Runge-Kutta-Merson method -- 6.3.9. Runge-Kutta-Lawson's fifth-order method -- 6.3.10. Runge-Kutta-Butcher sixth-order method -- 6.3.11. Runge-Kutta-Fehlberg method -- 6.4. Multi-step methods for IVP -- 6.5. Predictor-corrector methods -- 6.5.1. Milne-Simpson method -- 6.5.2. Adams-Bashforth-Moulton method -- 6.6. Systems of simultaneous ODE -- 6.7. Higher-order differential equations -- 6.8. Boundary-value problems -- 6.8.1. The shooting method -- 6.8.2. The nonlinear shooting method -- 6.8.3. The finite difference method -- 6.9. Summary -- 6.10. Exercises --
7. Eigenvalues and eigenvectors -- 7.1. Introduction -- 7.2. Linear algebra and eigenvalues problems -- 7.3. Diagonalization of matrices -- 7.4. Basic properties of eigenvalue properties -- 7.5. Some important results of eigenvalue problems -- 7.6. Numerical methods for eigenvalue problems -- 7.7. Vector iterative methods for eigenvalues -- 7.7.1. Power method -- 7.7.2. Inverse power method -- 7.7.3. Shifted inverse power method -- 7.8. Location of eigenvalues -- 7.8.1. Gerschgorin circles theorem -- 7.8.2. Rayleigh quotient -- 7.9. Intermediate eigenvalues -- 7.10. Eigenvalues of symmetric matrices -- 7.10.1. Jacobi method -- 7.10.2. Sturm sequence iteration -- 7.10.3. Given's method -- 7.10.4. Householder's method -- 7.11. Matrix decomposition methods -- 7.11.1. QR method -- 7.11.2. LR method -- 7.11.3. Upper Hessenberg form -- 7.11.4. Singular value decomposition -- 7.12. Summary -- 7.13. Exercises -- Appendices -- A. Some mathematical preliminaries -- B. Introduction to MATLAB -- C. Index of MATLAB programs -- D. Symbolic computation -- E. Answers to selected exercises -- F. About the CD-ROM -- Bibliography -- Index.

MATLAB.
Numerical analysis, Data processing.

9781934015230 (hardcover with cd-rom : alk. paper) 1934015237 (hardcover with cd-rom : alk. paper) 9780763773762 076377376X

515 B988i