Search Results

let $\quad-1=x_0 < x_1 <\ ...\ < x_n<1\quad$ be a set of abscissas and $\quad(y_0, y_1,\ ...\,y_n)\quad$ a sequence of the corresponding ordinates. Question: what can be said about the exi …

In general, approximation with least maximal error is possible with the Remez Algorithm. In your case I would suggest giving approximation with Chebyshev rational functions a try.

The following iterative algorithm may provide an efficient way of iteratively generating estimates with increasing precision for the optimal path: As the optimal path must be contained in a box $[x_0 …

This question is related to my question Differential Geometric Aspects of Rubber Bands, where I asked for a mathematical model of contracting rubber bands. In contrast to my former question, the situa …

An algorithm that works at least for dimensions $2$ and $3$ is: calculate a spanning tree of the $n$ points calculate the bisector planes of the spanning tree's edges the sought poiint is in the inte …

Spline interpolation requires the definition of boundary conditions because the smoothness requirements do not yield enough conditions for a unique solution. Question: which kind of boundary conditio …

What the PO actually is asking for, is how obtain the control points (or equivalently the wireframe) of a NURBS surface (the PO says "plane" instead of surface) from points on the surface (the black b …

To me, as an non-expert in the field, it seems as if numeric mathematics should have lost its importance because nowadays symbolic calculations or calculations with unlimited precision are generally a …

I have the task of finding a Chebyshev approximation for a time-series; I want to check different types of functions, e.g. polynomials, rational functions, harmonics, etc. I know that the Remez algori …

I have the task of determining approximations of a 2D function $f: (x,y)\in \mathbb{R}^2\mapsto\mathbb{R}$ from integrals along lines, i.e. from its Radon transform $R(\phi,\tau)[f(x,y)]$ and, because …

In a nutshell, the Moler and Morrison algorithm is a fast method for calculating euclidean distances in a numerically stable way by using reflections instead of the pythagorean theorem. In order t …

While checking an idea about knot-placement for spline interpolation, I needed to find a way to calculate splines, that are strictly monotone between adjacent pairs of knots and for which every knot i …

The Euler–Maclaurin formula states an interdependency between \begin{align} I\quad:=&\quad\int_m^nf(x) \, dx,\ \ m,n\in\mathbb{Z},\\[6pt] S\quad:=&\quad\sum_{k=m}^n f(k), \\[6pt] D\quad:=&\quad\left\l …

I recently faced the problem of efficiently approximating a very large set of data points and, neither having a model of the empiric function, nor of the error distribution, my method of choice would …

The interpolant $$A\left(e^{\frac{a}{A}(x-x_i)}-1\right)+B\cdot\left(\cosh\left(\frac{a}{A}(x-x_i\right)-1\right)+y_i\ =\ (A+B)\mathbf{e^{\frac{a}{A}(x-x_i)}}+B\cdot \mathbf{e^{-\frac{a}{A}(x-x_i)}}- …