Welcome

Interpolation

1. The best linear interpolator, Bli.doc, finds the optimal set of points for plotting a function.
Making an integral of this is discussed in BLI3.htm - This is the integration routine for finding G(r) in integration\MonteCarlo\Welcome.htm

2. In order to evaluate f(x) from this set of points, one needs to find J such that x(J) £ x £ x(J+1). This is accomplished by the subroutines (LOCATE.FOR, and LOCATE.C) described in Locate.doc.

3. Conversion of this file into a linear function is covered in FileFun.doc.

4. Once these points have been found Lagrange.doc is a good way to interpolate between these points to convert a collection of data points into a function.

5. Semi infinite range interpolation

Numerical Derivatives

Numerical derivatives are discussed in Derivatives.doc.

Findfun

Lagrange interpolation skipping a data point can be used to locate the largest error region. This can also be used in general error analysis. It is a bit more complicated findfun\Findfun.doc

Spline Interpolation

The derivatives of the interpolated function are discontinuous at the data points. A spline through these points has continuous first and second derivatives and discontinous third derivatives.

1. spline1.doc

2. spline2.doc

3. spline3.doc

4. Cubic Spline Interpolation .doc

..\wsteve\FDERS\The Lagrange Polynomial.htm Finds high derivatives for H-H potential.

LinearInterp.doc – very simple