CMSC 466: INTRODUCTION TO NUMERICAL ANALYSIS I

Catalog Description

Floating point computations, direct methods for linear systems, interpolation, solution of nonlinear equations. Listed also as MAPL 466. Credit will not be granted for both CMSC/MAPL 460 and CMSC/MAPL 466.

Objective

This course emphasizes understanding the theory behind the numerical algorithms. It is part of the two-course sequence 466-467.

Prerequisites

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

Topics

Floating point computations (1 week)
Properties of machine arithmetic, roundoff error.
Direct methods for linear systems (5 weeks)
Gaussian elimination, pivoting, Cholesky factorization, pivoting strategies, norms and matrix norms, conditioning and the effect of rounding error.
Interpolation (4 weeks)
Polynomial approximation, Newton and Lagrange form, error formula (derived), numerical differentiation (rounding error), quadrature (Newton-Cotes formulas).
Solution of nonlinear equations (4 weeks)
Bisection and fixed-point methods (one variable), Newton's method (1 variable), secant method (1 variable), Newton's method (several variables).

Course Text

K.E. Atkinson, An Introduction to Numerical Analysis, Wiley, New York, 1978.
S. Conte and C. DeBoor, Elementary Numerical Analysis, McGraw-Hill, New York, 1972.
Burden, Faires, and Reynolds, Numerical Analysis.

Typical Grading and Workload

60% - 2-3 exams
40% - 4-5 homeworks and projects