The Condition Number of a Class of Rayleigh-ritz-galerkin Matrices
نویسنده
چکیده
The purpose of this note is to study the Euclidean condition number of the matrix resulting from using the well-known RayleighRitz-Galerkin method with finite dimensional subspaces of polynomial spline functions to approximate the solution of a linear, selfadjoint* two-point boundary value problem. Roughly speaking, we consider a model class of such problems of order In and determine upper bounds, of the form of a constant times the norm of the partition associated with the spline subspace to the — 2wth power, for the Euclidean condition number of the associated matrix. The class of problems we are considering is defined by
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