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Are linear algorithms always good for linear problems? |
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| Authors: | Arthur G Werschulz Henryk Woźniakowski |
| Institution: | (1) Department of Computer Science, Columbia University, 10027 New York, NY, USA;(2) Department of Computer Science, Columbia University, 10027 New York, NY, USA;(3) Division of Science and Mathematics, Fordham University, College at Lincoln Center, 113 West 60th Street, 10023 New York, NY, USA;(4) Institute of Informatics, University of Warsaw, PKiN, Warsaw, Poland |
| 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. |
| Keywords: | Primary 65R20 68C05 68C25 Secondary 33J35 45B05 45L05 |
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