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Three points interpolation:

Three points interpolation:# Computation - 科学计算

r*s2005-04-05 07:04

1 楼

I have measured oscillatory temperature in three locations and I assume the
temperature varies linearly with length. How can I use these interpolation of
three ponits to obtain temperature at arbitrary location?

w*d2005-04-05 07:04

2 楼

linear interpolation needs 3pts in 2D, 4pts in 3D.
Also a linear function is not oscillatory.

【在 r*******s 的大作中提到】

: I have measured oscillatory temperature in three locations and I assume the
: temperature varies linearly with length. How can I use these interpolation of
: three ponits to obtain temperature at arbitrary location?

S*y2005-04-05 07:04

3 楼

interesting!
how to do multi-dimensional interpolations for arbitrary-shape meshes?

the
of

【在 w**d 的大作中提到】

: linear interpolation needs 3pts in 2D, 4pts in 3D.
: Also a linear function is not oscillatory.

w*d2005-04-05 07:04

4 楼

It is quite difficult.
For 1D, n distinct points can guarantee a degree n-1 interpolated polynomials,
the quality (accuracy) depends on the distribution though. Babuska and Chen Q.
gave the 1D optimal points set in a paper in 1995.
For multi-dimensional interpolation, it is even not easy to guarantee
the Vandermonde matrix is non-singular. In one of Yau's paper, he showed
the matrix is non-singular when the points are distributed in a certain way.
(I did not read that paper.)

【在 S***y 的大作中提到】

: interesting!
: how to do multi-dimensional interpolations for arbitrary-shape meshes?
:
: the
: of