Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Error estimates for some variational methods applicable to scattering and radiation problems

Author: M. Szałek
Journal: Quart. Appl. Math. 27 (1970), 473-479
DOI: https://doi.org/10.1090/qam/256637
MathSciNet review: 256637
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Abstract | References | Additional Information

Abstract: We consider variational expressions helpful in calculating the approximate value of a scalar product, in Hilbert space, of an arbitrary vector $ g$ with a solution $ u^\circ $ of an arbitrary inhomogeneous linear equation. Error bounds for this approximate value are given. For the case where an approximate solution of an inhomogeneous equation is sought in an arbitrary subspace of a space containing $ u^\circ $, conditions are specified for a best estimate of the error by the use of two trial vectors. A method is presented for an additional improvement of the error estimate by using four trial vectors.

References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/qam/256637
Article copyright: © Copyright 1970 American Mathematical Society

American Mathematical Society