Path: utzoo!attcan!uunet!cs.utexas.edu!tut.cis.ohio-state.edu!ucsd!ogccse!emory!wuarchive!texbell!sequoia!rpp386!woody
From: woody@rpp386.cactus.org (Woodrow Baker)
Newsgroups: comp.graphics
Subject: Re: Spline coefficients
Summary: Splines
Keywords: matrix problem, help
Message-ID: <17342@rpp386.cactus.org>
Date: 21 Nov 89 12:51:23 GMT
References: <352@texhrc.UUCP> <12349@watcgl.waterloo.edu>
Organization: River Parishes Programming, Plano, TX
Lines: 50

In article <12349@watcgl.waterloo.edu>, rhbartels@watcgl.waterloo.edu (Richard Bartels) writes:
> In article <352@texhrc.UUCP> bls@texhrc.UUCP (Brian L. Sumner) writes:
> >
> >I am tring to determine a set of spline coefficients, and to do
> >so I need to solve the linear system
> >    Ax = b
> >where A can be a very large (positive definite?) banded matrix.
> >
> >[   ... description deleted ... ]
> >
> 
> The description sounds suspiciously like the sort of matrix that arises
> from interpolating or fitting over a rectilinear mesh (a tensor-product grid).
> If this is the case, then deBoor's book, "A Practical Guide to Splines"
> and the following two articles might be instructive.  Briefly, a tensor-product
> problem in n dimensions can be reduced to n successive one-dimensional
> problems.  With B-splines, a each one-dimensional problem interpolation
> problem, for example, typically involves a k-banded matrix, where k is the
> degree of the spline; e.g.,  cubics involve tridiagonal matrices.
> Such systems can be solved in linear time.  deBoor's book offers code
> (also available on NETLIB), and the articles show how the tensor-product
> insight extends to least squares fitting (as well as being more readible
> than the explanation given by deBoor).
> 
> -Richard
> ==========================================================================
> %A P. Dierckx
> %L Dierckx77-
> %T An algorithm for least-squares fitting of cubic spline surfaces
> to functions on a rectilinear mesh over a rectangle
> %J Journal of Computational and Applied Mathematics
> %V 3
> %N 2
> %D 1977
> %P 113-129
> %l journal-article
> 
> %A P. Dierckx
> %L Dierckx81-
> %T An Algorithm for Surface-Fitting with Spline Functions
> %J IMA Journal of Numerical Analysis
> %V 1
> %D 1981
> %P 267-283
> %l journal-article

How do you access NETLIB.  I'd like specific details, as I am sort of a
novice at using the net at this time.  Can post or email, or call.  Thanks

Woody Baker (512)-837-8317