An Introduction to Numerical Analysis for Electrical and Computer Engineers
Chapter One
Functional Analysis Ideas
1.1 INTRODUCTION
Many engineering analysis and design problems are far too complex to be solved
without the aid of computers. However, the use of computers in problem solving
has made it increasingly necessary for users to be highly skilled in (practical)
mathematical analysis. There are a number of reasons for this. A few are as follows.
For one thing, computers represent data to finite precision. Irrational numbers
such as [pi] or [square root of 2] do not have an exact representation on a digital computer (with the
possible exception of methods based on symbolic computing). Additionally, when
arithmetic is performed, errors occur as a result of rounding (e.g., the truncation of
the product of two n-bit numbers, which might be 2n bits long, back down to n
bits). Numbers have a limited dynamic range; we might get overflow or underflow
in a computation. These are examples of finite-precision arithmetic effects. Beyond
this, computational methods freq ... read full excerpt from An Introduction to Numerical Analysis for Electrical and Computer Engineers ebook
