Approximation
The Problem: given data (x,f(x)) for x in a set X
a function g(x,P) , and a norm ||.|| on X
find parameters P such that
||f(.)-g(.,P)||is minimal with respect to P
For approximations to special functions search the netlib-libraries a, amos, cephes, elefunt, specfunc and the file netlib/toms/757 .
Here a list of some representative approximation algorithms is given. There are many more possibilities, e.g. using interpolation by splines, by splines under tension, by radial basis functions .... For more information use the search facility of netlib
NETLIB
or the HOTGAMS service
HOTGAMS
| APPROX/EXCH | best polynomial approximation to a discrete one-dimensional data set in the Chebyshev (minimax) sense |
| L1GNR | generating test problems for discrete linear l1-approximation |
| CDFCOR | rational approximation to a finite set of data f90 version |
| COCA | Complex linear Chebyshev Approximation (Matlab) |
| l2appr | construct least squares approximation of B-splines to given data |
| l2main | driver for l2appr.f |
| titan | sample data for l2appr.f |
| cubgcv | cubic spline data smoother using cross validation (used to produce the picture above) |
| APPROX | discrete linear l1 approximation |
| STL2 | approximation by a piecewise linear function |
| CL1(B&R) | linearly constrained approximation in l1-sense by linear programming |
| CL1(B&C) | overdetermined system, linear constraints, discrete approximation in l1 sense |
| RQN | unconstrained l1 approximation, interior point (several nonstandard languages) |
| DIFCOR | rational approximation to finite set of data (differential correction algorithm) |
| DIFCORDOC | documentation for difcor |
| REMEZ | continuous minimax rational approximation (in C) |
| EVAL | needed by REMEZ (in C) |
| CSHEP2D | Cubic {Shepard} Method for Bivariate Interpolation of Scattered Data |
| TSHEP2D | Cosine Series {Shepard} Method for Bivariate Interpolation of Scattered Data |
| CS2TST | accuracy tests for interpolation of scattered planar data |
| PCB2NURB | smooth free form surfacing with linearly trimmed bicubic B-splines |
| SSRFPACK | Interpolation of Scattered Data on the Surface of a Sphere with Splines under Tension |
| SDBI3P | Scattered-data surface fitting that has the accuracy of a cubic polynomial |
| TSPACK | tension spline curve-fitting package |
| QSHEP2D | quadratic Shepard method for bivariate interpolation of scattered data |
| CUBGCV | O(n) computation of a cubic smoothing spline fitted to n noisy data points |
| CAPROX | Chebyshev solution of systems of complex linear equations with linear inequality constraints and simple bound constraints |
| CONST&EVAL | fitting multinomials in the least squares sense |
| LibLip | scattered interpolation with Lipschitz interpolants (Unix/Linux/Win) |
