Rate of convergence of Lawson's algorithm

The algorithm of Charles L. Lawson determines uniform approximations of functions as limits of weighted ${L_2}$ approximations. Lawson noticed from experimental evidence that the algorithm seemed to converge linearly and convergence was related to a factor which was the ratio of the largest nonmaximum error of the best uniform approximation to the maximum error. This paper proves the linear convergence and explores the relation of the rate of convergence to this ratio.