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Are linear algorithms always good for linear problems?

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Abstract

We exhibit linear problems for which every linear algorithm has infinite error, and show a (mildly) nonlinear algorithm with finite error. The error of this nonlinear algorithm can be arbitrarily small if appropriate information is used. We illustrate these examples by the inversion of a finite Laplace transform, a problem arising in remote sensing.

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Authors and Affiliations

  1. Department of Computer Science, Columbia University, 10027, New York, NY, USA

    Arthur G. Werschulz & Henryk Woźniakowski

  2. Department of Computer Science, Columbia University, 10027, New York, NY, USA

    Arthur G. Werschulz & Henryk Woźniakowski

  3. Division of Science and Mathematics, Fordham University, College at Lincoln Center, 113 West 60th Street, 10023, New York, NY, USA

    Arthur G. Werschulz & Henryk Woźniakowski

  4. Institute of Informatics, University of Warsaw, PKiN, Warsaw, Poland

    Arthur G. Werschulz & Henryk Woźniakowski

Authors
  1. Arthur G. Werschulz
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  2. Henryk Woźniakowski
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Werschulz, A.G., Woźniakowski, H. Are linear algorithms always good for linear problems?. Aeq. Math. 31, 202–212 (1986). https://doi.org/10.1007/BF02188189

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  • DOI: https://doi.org/10.1007/BF02188189

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