CMSC 460 COMPUTATIONAL METHODS

Catalog Description

Basic computational methods for interpolation, least squares, approximation, numerical quadrature, numerical solution of polynomial and transcendental equations, systems of linear equations and initial value problems for ordinary differential equations. Emphasis on the methods and their computational properties rather than on their analytic aspects. Listed also as MAPL 460. Credit will not be granted for both CMSC/MAPL 460 and CMSC/MAPL 466.

Objective

This course emphasizes intelligent use of mathematical software packages. It is meant to be a terminal course.

Prerequisites

MATH 240 and MATH 241; CMSC 110 or CMSC 113.

Topics

  1. Introduction, Computer Arithmetic and Errors (1.5 weeks)

    Machine arithmetic, error analysis, stability and conditioning.

  2. Solving Linear Systems of Equations (2 weeks)

    Gaussian elimination, SGEFS and Fortran array handling, well-conditioning vs. ill-conditioning, matrix and vector norms, sparse systems: direct and iterative methods.

  3. Interpolation (2 weeks)

    Polynomial interpolation, piecewise polynomial interpolation, spline interpolation.

  4. Integration and Differential Equations (4 weeks)

    Elementary integration formulas (midpoint, trapezoid, etc.), compound and adaptive integration formulas: QIDA, QK15, PCHQA, ordinary differential equations and Euler's method, adaptive methods for ordinary differential equations: SDRIV2, methods for stiff systems.

  5. Solving Nonlinear Systems of Equations (2 weeks)

    bisection, Newton's method, and secant method: FZERO; methods for systems of equations: SNSQE.

  6. Solving Linear Least Squares Problems (1 week)

    data-fitting and least squares, QR factorization: SQRLS.

  7. Optimization and Nonlinear Least Squares (time permitting)

Course Text

David Kahaner, Stephen Nash, and Cleve Moler, Numerical Methods and Software, Prentice Hall, 1988.

Typical Grading and Workload