Adaptivel1-l2 curve fitting

In References 1 and 2, algorithms were introduced for adaptively computing smooth piecewise polynomial approximations using uniform, least-squars (l2) and restricted-range uniform approximations. This present paper introduces a FORTRAN program for computing smooth piecewise polynomial approximations to data and/or precise mathematical functions (in discrete form) which allows the user the option of using best l1 of best l2 approximations. (The l2 option of this newly developed l1–l2 adaptive curve-fitting package supersedes the code listed in Reference 1 for the old least-squares program.) In this paper, adaptive curve-fitting algorithm used in this l1–l2 package is described in detail, the FORTRAN program is the given (in the Appendix) and discussed, the numerical results are presented in an effort to illustrate how the l1 and l2 versions of this algorithm may be used most effectively.