FAQFAQ   SearchSearch   MemberlistMemberlist   UsergroupsUsergroups 
 ProfileProfile   PreferencesPreferences   Log in to check your private messagesLog in to check your private messages   Log inLog in 
Forum index » Science and Technology » Math » num-analysis
2D Lagrangian interpolation
Post new topic   Reply to topic Page 1 of 1 [1 Post] View previous topic :: View next topic
Author Message
deltaquattro@gmail.com
science forum beginner


Joined: 21 Jul 2006
Posts: 1

PostPosted: Fri Jul 21, 2006 1:57 pm    Post subject: 2D Lagrangian interpolation Reply with quote

Hi,

I would like to perform 2D quadratic interpolation of a function. The
function values are known over a grid which for now is Cartesian
uniform. Requirements in order of importance:
1) I must write the interpolation subroutine myself, so it must be
simple;
2) I'd like to evaluate the coefficients of the interpolating
polynomial, since I may need its derivatives;
3) finally, I'd like the method to work also on a grid with possibly
local anisotropic refinement (for example, square cells of side dx,
with two neighboring rectangular cells of smaller side dx/2). That's
not too important, anyway.
In your opinion, which method is best amongst the following, for what
it concerns accuracy and coding simplicity?
1) Quadratic interpolation over a 6 node simplex, performed by writing
the Vandermonde system, solving it with LU and finally evaluating the
polynomial with Horner's method (how is this performed for multivariate
polynomials?). I know the condition number grows exponentially with the
number of nodes, but since I only use a 2nd degree polynomial, maybe
that's not so bad.
2) Quadratic interpolation over simplex using shape functions and
barycentric coordinates.
3) As 1), but using least square interpolation over at least six
surrounding nodes (good for possible future extension to
anisotropically refined grids). Is it better to do perform least square
interpolation with shape functions, i. e. as in 2)?
4) Another method suggested by you, possibly as simple as the ones I
presented, otherwise I may not be able to code it myself Smile
Well, that's all, I look forward for an answer of yours,

Greetings,

deltaquattro (Sergio Rossi)
Back to top
Google

Back to top
Display posts from previous:   
Post new topic   Reply to topic Page 1 of 1 [1 Post] View previous topic :: View next topic
The time now is Thu Jun 29, 2017 3:49 pm | All times are GMT
Forum index » Science and Technology » Math » num-analysis
Jump to:  

Similar Topics
Topic Author Forum Replies Last Post
No new posts Problems with interpolation of near zero values deltaquattro num-analysis 0 Mon Jun 19, 2006 1:29 pm
No new posts 2D interpolation ? How? Martin Jørgensen num-analysis 6 Sat May 27, 2006 3:11 pm
No new posts Closed Periodic B-Spline Interpolation jaisingh@adelphia.net Math 0 Mon May 22, 2006 7:37 am
No new posts new interpolation algorithms kjinnovation@earthlink.ne num-analysis 0 Wed May 17, 2006 4:15 pm
No new posts cubic Hermite splines for interpolation franz.bauer78@yahoo.de Math 0 Tue May 16, 2006 10:33 am

Copyright © 2004-2005 DeniX Solutions SRL
Other DeniX Solutions sites: Electronics forum |  Medicine forum |  Unix/Linux blog |  Unix/Linux documentation |  Unix/Linux forums  |  send newsletters
 


Powered by phpBB © 2001, 2005 phpBB Group
[ Time: 0.0314s ][ Queries: 16 (0.0046s) ][ GZIP on - Debug on ]