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ERROR ESTIMATES FOR SOME VARIATIONAL METHODS APPLICABLE TO SCATTERING AND RADIATION PROBLEMS
Quarterly of Applied Mathematics
Vol. 27, No. 4 (JANUARY 1970), pp. 473-479
Published by: Brown University
Stable URL: http://www.jstor.org/stable/43636053
Page Count: 7
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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° 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°, 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.
Quarterly of Applied Mathematics © 1970 Brown University