An Introduction to Numerical Computations

This introduction to modern numerical methods encourages students in mathematics, physics, engineering, computer science or physical science to develop computational intuition and self-reliance by comparing the performance of various methods in solving a given problem. Number representation and round-off are presented in a hypothetical computer decimal word, instead of in binary representation, to simplify the explanation of origins and propagation of round-off error. Linear equations are studied directly after the general topics of round-off and error propagation. New optional sections include explanation and demonstration of Fourier and differential equation methods for analyzing linear systems in either state space or block diagram representations. Recent developments are reflected in material covering computational practice in an expanded eigenvalue section, and the discrete Fourier transform, with its application to filtering, is explained.