Schultz, Martin H. (1969) Approximation Theory of Multivariate Spline Functions in Sobolev Spaces. SIAM Journal on Numerical Analysis, 6 (4). pp. 570-582. ISSN 0036-1429. http://resolver.caltech.edu/CaltechAUTHORS:20120921-134826749
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In this paper we study some approximation theory questions which arise from the analysis of the discretization error associated with the use of the Rayleigh-Ritz-Galerkin method for approximating the solutions to various types of boundary value problems, cf. [13, , [33, [43, , , [93, , [143, , ,  and . In particular, we consider upper and lower bounds for the error in approximation of certain families of functions in Sobolev spaces, cf. , by functions in finite-dimensional "polynomial spline types" subspaces, cf. . In doing this, we directly generalize, improve, and extend the corresponding results of, , , , , and . Throughout this paper, the symbol K will be used repeatedly to denote a positive constant, not necessarily the same at each occurrence and the symbol μ will be used repeatedly to denote a nonnegative, continuous function on [0,∞], not necessarily the same at each occurrence.
|Additional Information:||© 1969 SIAM. Received by the editors May 22, 1969, and in revised form July 17, 1969. This work was supported in part by the National Science Foundation under Grant GP-11236.|
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|Deposited By:||Jason Perez|
|Deposited On:||21 Sep 2012 23:33|
|Last Modified:||26 Dec 2012 16:14|
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