ABSTRACT
In this chapter, we present a number of everyday life problems whose solutions need the application of linear approximation, which is the subject of this book. The problems presented here occur in social sciences, economics, industry and digital image processing. In the following, we assume that mathematical models have been agreed upon, that observed data have been collected constituting the columns of a matrix A, and that the response data constitute vector b. The solution of the problem, vector x, is the solution vector of the matrix equation
Ax = b The n by m, n > m, matrix A consists of n observations in m
parameters. Because of measuring errors in the elements of matrix A and in the response n-vector b, a larger number of observations than the number of parameters are collected. Thus system Ax = b is an overdetermined system of linear equations.
