Algorithm 770: BVSPIS - a package for computing boundary-valued shape-preserving interpolating splines.
1. GENERAL DESCRIPTION
This article describes the package BVSPIS which is a Fortran 77 implementation of the method introduced in Costantini  and which is provided both in single- and in double-precision versions.
The package is divided in two main parts. The first part is made up of modules designed for computing a [C.sup.k], k = 1, 2, polynomial spline of degree n, n [greater than or equal to] 3k, interpolating an arbitrary set of data points ([x.sub.i], [y.sub.i]), i = 0, 1, ..., [N.sub.p]. By properly setting the corresponding control parameters, it is possible to preserve the monotonicity and/or convexity in a local or global way, to optionally satisfy boundary conditions of the form
[Mathematical Expression Omitted]
or, given a continuous, invertible function [Beta]: IR [approaches] IR,
s[prime]([x.sub.Np]) = [Beta](s[prime]([x.sub.0])).
In addition, when the continuity k = 2 is required, we have
[Mathematical Expression Omitted].
Since, in general, the interpolating spline is not unique, it is possible to select, among the set of all feasible solutions, the one whose derivatives at the knots are the closest to a (in some sense optimal), target input sequence. The structure of this part of the code is described in Figure 1.
The second part of the code consists of a set of modules that evaluate the spline and/or its first and/or second derivative at a specified sequence of tabulation points, using a sequential or a binary search scheme. This second part of the code can be activated several times during the same job, but, of course, must follow an execution of the first part. The structure of the second part of the code is described in Figure 2.
COSTANTINI, P. 1997. Boundary-valued shape-preserving interpolating splines. ACM Trans. Math. Softw. 23, 2 (June). This issue.
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|Title Annotation:||Boundary-Valued Shape-Preserving Interpolating Spline|
|Publication:||ACM Transactions on Mathematical Software|
|Date:||Jun 1, 1997|
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