Tchebycheff approximation on a discrete point set: algorithms old and new

Several linear and nonlinear algorithms for solving the discrete Tchebycheff problem are compared in this study. The Lawson algorithm is compared with two more well-known methods of linear Tchebycheff approximation. A new acceleration scheme for the Lawson algorithm is introduced and its performance is tested with an already existing acceleration technique. The new version is found to be better than the previous one but not as effective as the traditional Exchange method. A nonlinear version of Lawson\u27s algorithm is proposed for the solution of problems having approximating functions which are varisolvent. Some linear theorems of Lawson are extended to the nonlinear case. A modification of Osborne and Watson\u27s nonlinear method is introduced and tested on five problems. This new technique improves the efficiency remarkably, particularly for larger problems --Abstract, page ii