Abstract
Suppose we seek the solution x* ɛ X of an ill-posed problem which can be formulated as an infinite system of scalar equations: λj(x) = ßj (j = 1,2,…). The method of generalized interpolation defines approximants xN minimizing ‖x‖ among solutions of the finite system: λj (x) = ßj (j = 1,…,N). Under quite mild conditions one has xN → x*, even when the method is modified for computational convenience.
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© 1986 Birkhäuser Verlag Basel
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Seidman, T.I. (1986). The Method of ‘Generalized Interpolation’ for Approximate Solution of Ill-Posed Problems. In: Cannon, J.R., Hornung, U. (eds) Inverse Problems. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 77. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7014-6_12
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DOI: https://doi.org/10.1007/978-3-0348-7014-6_12
Publisher Name: Birkhäuser Basel
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