Report 1995-16

On a Recovery Problem

M.D. Buhmann and A. Pinkus

Abstract: This paper concerns itself with the recovery of the coefficients, shifts and, where applicable, dilates of a given form $$f(\bfx) = \sum^m_{j=1} c_j \;G(\bfx- \bft_j)\,, {\rm \ or\ \,} f(\bfx) = \sum^m_{j=1} c_j \;g(\bfa_j \cdot \bfx - b_j)\,, \quad \bfx\in \RR^n,$$ where emf/em, emG/em and emg/em are known. That is, we provide a method that identifies the quantities $c_j$, $\bft_j$, $\bfa_j$ and $b_j$. In some cases we can even find emG/em given only emf/em and knowing that emf/em is of the above form.

Keywords: scalar advection equation, difference scheme,accuracy, stability, order star, algebraic function, Riemann surface

Paper: Available as PDF (200 KB) or as hardcopy to order reports@sam.math.ethz.ch.

Publishing information: Annals of Numerical Mathematics, 4, (1996), pp. 129-142