Restricted Chebyshev Approximation

C = (cij) is a given real n by m matrix of rank k, k ≤ m < n and f = (fi) is a given real n-vector. The Chebyshev solution of this system is the m-vector a = (ai) that minimizes the Chebyshev norm z of the residual vector r (13.1.1) z = max|ri|, i = 1, 2, …, n

where ri is the ith residual (error) and is given by

(13.1.2) , i = 1, 2, …, n

Note that ri here is –ri in (10.1.3).