A Caltech Library Service

Approximation Theory of Multivariate Spline Functions in Sobolev Spaces

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. doi:10.1137/0706052.

PDF - Published Version
See Usage Policy.


Use this Persistent URL to link to this item:


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, [2], [33, [43, [7], [8], [93, [12], [143, [18], [19], [20] and [22]. In particular, we consider upper and lower bounds for the error in approximation of certain families of functions in Sobolev spaces, cf. [15], by functions in finite-dimensional "polynomial spline types" subspaces, cf. [16]. In doing this, we directly generalize, improve, and extend the corresponding results of[1], [17], [18], [19], [20], and [21]. 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.

Item Type:Article
Related URLs:
URLURL TypeDescription
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.
Funding AgencyGrant Number
Issue or Number:4
Record Number:CaltechAUTHORS:20120921-134826749
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:34286
Deposited On:21 Sep 2012 23:33
Last Modified:09 Nov 2021 23:07

Repository Staff Only: item control page