CXFTV2: A Fortran subroutine for the discrete least squares convex approximation

✍ Scribed by I.C. Demetriou

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 824 KB
• Volume: 100
• Category: Article
• ISSN: 0010-4655
• DOI: 10.1016/s0010-4655(96)00158-0

✦ Synopsis

A Fortan subroutine calculates the least squares approximation to n data values con~n~ag ~ erro~ ~ to non-negative second divided differences (convexity). The method employs a dual active set qua~ta~ technique that allows several corcavities of an iterate to ,he corrected simul~..eo'~ly, whk:h is a d~hu:ti~e ~ of ~h~ calculation. A B-spti .he ¢e~.nce~entation of the iL~rates reduces each active set cakuie~ to an uncot~,~m~ine~ nfi~ with fe~er variables tha~ requires only O(n) computer operations. Details of these g'chniqces ~aci~lgBg ~ ~ sg~ that es,ablishes the implementation of the method ~ s~secified. Numerical testing on a variety of data se~ ~ ~ tl~ subroutine is particularly efficient, terminating after a small number of active set changes, em subcou¢ine ~h~g s~u~L~ f~ large numbers of data. A numerical example ~d its o~tput is provided to help the use of the softwa:e.