منابع مشابه
Matrix Representations by Means of Interpolation
We examine two different matrix representations of curves and surfaces based on or constructed by interpolation through points. Both are essentially implicit representations of objects given as parametric models or given as a point cloud, and both are quite powerful since they reduce geometric operations to linear algebra. First, we examine a representation by interpolation matrices, developed ...
متن کاملMeans and Hermite Interpolation
Let m2 < m1 be two given nonnegative integers with n = m1+m2+1. For suitably differentiable f , we let P,Q ∈ πn be the Hermite polynomial interpolants to f which satisfy P (a) = f (a), j = 0, 1, ..., m1 and P (b) = f (b), j = 0, 1, ..., m2, Q (a) = f (a), j = 0, 1, ..., m2 and Q(b) = f (b), j = 0, 1, ..., m1. Suppose that f ∈ C (I) with f (x) 6= 0 for x ∈ (a, b). If m1 − m2 is even, then there ...
متن کاملCOMPOSITE INTERPOLATION METHOD AND THE CORRESPONDING DIFFERENTIATION MATRIX
Properties of the hybrid of block-pulse functions and Lagrange polynomials based on the Legendre-Gauss-type points are investigated and utilized to define the composite interpolation operator as an extension of the well-known Legendre interpolation operator. The uniqueness and interpolating properties are discussed and the corresponding differentiation matrix is also introduced. The appl...
متن کاملInterpolation Problem in Nevanlinna Classes
The abstract interpolation problem (AIP) in the Schur class was posed V. Katznelson, A. Kheifets and P. Yuditskii in 1987 as an extension of the V.P. Potapov’s approach to interpolation problems. In the present paper an analog of the AIP for Nevanlinna classes is considered. The description of solutions of the AIP is reduced to the description of L-resolvents of some model symmetric operator as...
متن کاملLinear interpolation problems for matrix classes and a transformational characterization of M-matrices
The linear interpolation problem (LIP) for a class of matrices C asks for which pairs of vectors x, y there exists a matrix A ∈ C such that Ax = y. The LIP is solved for M-matrices, P-matrices, H-matrices, and H+-matrices. In addition, a transformational characterization is given for M-matrices that refines the known one for P-matrices. There is no such characterization for Hor H+-matrices. © 2...
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ژورنال
عنوان ژورنال: Banach Journal of Mathematical Analysis
سال: 2015
ISSN: 1735-8787
DOI: 10.15352/bjma/09-3-10