New Preconditioning Interpolation Scheme

[Namir]

After working earlier this year on several projects based on my polynomials with fractional powers, I turned my attention and curiosity towards interpolation with fractional-powered polynomials. One option is to use build Vandermonde style matrix and take it from there. The other approach was to simply supply x with fractional powers. After trying to figure out why this approach seems to work wel in general, I resorted to plotting (x,y) and (x^p,y) and comparing the two curves (for example for y=ln(x)), The data for (x^0.1, ln(x)) gave a curve with very little curvature, compared to (x, ln(x)). Using Excel calculations confirmed that the (x^0.1, ln(x)) data had a higher correlation coefficient for a linear regression than did (x, ln(x)).

Namir