Research Catalog

Title

Fundamentals of computer numerical analysis / Menahem Friedman, Abraham Kandel.

Author

Friedman, Menahem.

Publication

Boca Raton [Fla.] : CRC Press, [1994], ©1994.

Items in the Library & Off-site

Holdings

Details

Additional Authors

Kandel, Abraham.

Description

xi, 587 pages : illustrations; 25 cm +

Alternative Title

Computer numerical analysis.

Subject

• Electronic data processing
• Numerical analysis > Data processing

Note

• System requirements for the computer disk: FORTRAN-77.

Bibliography (note)

• Includes bibliographical references (p. 527-529) and index.

Contents

• 1. Introduction. 1.1. What is Numerical Analysis? 1.2. Algebraic Representation and Arithmetic with Complex Numbers. 1.3. Geometric Interpretation. 1.4. Polynomials. 1.5. Taylor Series. 1.6. Elementary Functions of a Complex Variable. 1.7. Functions of Several Variables and Partial Derivatives -- 2. Error. 2.1. Representation of Numbers and Conversions. 2.2. Floating Point Numbers. 2.3. Definitions and Sources. 2.4. Error Propagation. 2.5. Summation -- 3. Iteration. 3.1. Definition of an Iteration Problem and the Standard Iteration Method. 3.2. Rate of Convergence. 3.3. Aitken's Method for Acceleration. 3.4. Steffensen's Modification (STM). 3.5. Newton's Method: Advantages and Limitations. 3.6. Related Schemes and Modifications to Newton's Method. 3.7. Extensions to Multivariable Systems -- 4. Linear Difference Equations. 4.1. General Concepts. 4.2. Homogeneous Difference Equations of Order 2. 4.3. The General Solution to AX = B. 4.4. Linear Difference Equations of Order N.
• 4.5. The Backward Difference Operator. 4.6. Application: Bernoulli's Method -- 5. Interpolation and Approximation. 5.1. Lagrange's Interpolator. 5.2. Error Estimate. 5.3. Convergence to the Interpolated Function. 5.4. Divided Differences. 5.5. Interpolation by Splines. 5.6. Approximations of Functions. 5.7. Chebyshev Polynomials. 5.8. Near Minimax Approximation. 5.9. Least-Squares Approximation. 5.10. Other Approximations -- 6. Numerical Integration and Differentiation. 6.1. Numerical Integration: The Trapezoidal and Simpson Rules. 6.2. Gaussian Integration. 6.3. The Romberg Method. 6.4. Multiple Integrals. 6.5. Numerical Differentiation -- 7. Linear Equations. 7.1. System of Linear Equations: Matrices. 7.2. Gaussian Elimination. 7.3. LU Factorization. 7.4. Iterative Methods. 7.5. Error and Stability. 7.6. The Eigenvalue Problem -- 8. Numerical Solutions of Differential Equations. 8.1. Preliminaries. 8.2. Euler's Method. 8.3. Taylor's Method. 8.4. Runge-Kutta Methods.
• 8.5. Error Control: Runge-Kutta-Fehlberg Method. 8.6. Multistep Methods. 8.7. Stability of Numerical Methods. 8.8. Systems of Differential Equations -- 9. Numerical Solutions of Partial Differential Equations. 9.1. Various Types of Partial Differential Equations. 9.2. Analytical Solutions I: Fourier Series. 9.3. Analytical Solutions II: Separation of Variables. 9.4. Finite Differences: Parabolic Partial Differential Equations. 9.5. Finite Differences: Hyperbolic Partial Differential Equations. 9.6. Finite Differences: Elliptic Partial Differential Equations. 9.7. Finite Elements -- List of Algorithms and Numerical Methods.

ISBN

0849386373 (acid-free paper)

LCCN

92039853

OCLC

• 26974579
• ocm26974579

Owning Institutions

Columbia University Libraries