On Condition Numbers Associated with Radial-Function Interpolation
نویسندگان
چکیده
منابع مشابه
Error estimates and condition numbers for radial basis function interpolation
For interpolation of scattered multivariate data by radial basis functions, an \uncertainty relation" between the attainable error and the condition of the interpolation matrices is proven. It states that the error and the condition number cannot both be kept small. Bounds on the Lebesgue constants are obtained as a byproduct. A variation of the Narcowich{Ward theory of upper bounds on the norm...
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where α = (α1, . . . , αn) is an n-tuple of nonnegative integers and |α| = ∑n j=1 |αj |. If every polynomial p ∈ πm−1(R) is determined by its values on X, then we will say that the data set X is unisolvent (for πm−1(R )). This condition can also be rephrased in terms of matrices. Order the monomials x in some convenient way. Form the matrix P for which the rows are an x evaluated at xj , j = 1,...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1994
ISSN: 0022-247X
DOI: 10.1006/jmaa.1994.1311