Are linear algorithms always good for linear problems? Research Papers Received: 26 February 1985 Revised: 13 November 1985 DOI:
Cite this article as: Werschulz, A.G. & Woźniakowski, H. Aeq. Math. (1986) 31: 202. doi:10.1007/BF02188189 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.
AMS (1980) subject classification Primary 65R20, 68C05, 68C25 Secondary 33J35, 45B05, 45L05 References
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Werschulz, A. G., What is the complexity of ill-posed problems?. In preparation.
Werschulz, A. G., Optimal residual algorithms. In preparation.