Fundamentals of Minterpy#
This section provides a detailed explanation of the mathematical foundation behind Minterpy.
The problem
The polynomial interpolation problem is central to Minterpy.
Revisit the polynomial interpolation problem and its connection to approximation on this page.
Representing polynomials
Polynomials can be expressed as a linear combination of a set of polynomials called the basis polynomials.
Review the polynomial bases supported by Minterpy on this page.
Getting interpolating polynomials
With a careful consideration, a polynomial that interpolate a given function can be constructed.
Review the essential components required to build an interpolating polynomial on this page.
Evaluating polynomials
Once a polynomial is obtained, how can it be evaluated at an arbitrary query point?
The answer depends on the basis in which the polynomial is represented.
Changing polynomial basis
A polynomial expressed in one basis may be expressed in another. Depending on the purpose, some representations may be better than the others.
On this page, the theorems behind such a transformation are presented.
Polynomial based on scattered data
Stable polynomial interpolation requires a careful selection of interpolation points; but what if scattered data is provided instead?
Using the least squares method, you can still construct a polynomial from the data.
Advanced topics