ABSTRACT
C = (cij) is a given real n by m matrix of rank k, k ≤ m < n, f = (fi) is a given real n-vector and a = (aj) is the m-solution vector. The residual vector for this system is given by
r = Ca – f In the last four chapters, algorithms are presented for four kinds of
linear Chebyshev approximations. In Chapter 10, the ordinary Chebyshev approximation of system Ca = f is presented, where the Chebyshev norm of the residual vector r is minimum [1]. In Chapter 11, the one-sided Chebyshev approximation of system Ca = f requires the additional constraints that all the elements of the residual vector r be either non-positive or non-negative. In Chapter 12, the bounded Chebyshev approximation is presented, where the additional constraints are that each element of the solution vector a is bounded between 1 and –1. In Chapter 13, different additional constraints are that the left hand side of system Ca = f, i.e., vector Ca be bounded between lower and upper rages. The solution vector a in any of the aforementioned Chebyshev algorithms, if it exists, may or may not be unique.
