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On a Recovery Problem

by M. D. Buhmann and A. Pinkus

(Report number 1995-16)

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

@Techreport{BP95_183,
  author = {M. D. Buhmann and A. Pinkus},
  title = {On a Recovery Problem},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1995-16},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1995/1995-16.pdf },
  year = {1995}
}

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