Titlebook: Spline Functions and Multivariate Interpolations; B. D. Bojanov,H. A. Hakopian,A. A. Sahakian Book 1993 Springer Science+Business Media B.

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Multivariate Mean Value Interpolation,Let ..,... ,..} ∈ ℝ be an arbitrary set of knots (not necessarily distinct) and µ. := {.. = ..} - the multiplicity of the point .. in .. The . of a function . is defined as a unique polynomial .. µπr (ℝ) satisfying (see Chapter 1) . where .., ..,...,.., are all the distinct points in ..

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Multivariate Pointwise Interpolation,In this chapter, we consider the problem of interpolation of values of a function and its partial derivatives by multivariate polynomials from a certain finite-dimensional space. The interpolation problem consists of the following components:

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Interpolation by Algebraic Polynomials,ing attached to these words was that he could construct explicitly the algebraic polynomial of arbitrary degree . which assumes preassigned values ..,..., .. at given points .. < ... < ... Newton described this method in 1687 in the third book of his famous “Principia”. This is the way classical interpolation theory was born.

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Natural Spline Functions,om π.. We shall denote by ..(..,..., ..) the class of natural spline functions of degree 2. - 1 with knots .. It is clear that ..(..,..., ..) consists of all splines . from ..(..,..., ..) which satisfy the boundary conditions:

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Monosplines,tiplicities ..,..., .. respectively, is any expression of the form . with real coefficients {..} and {..}, 1 ⩽ .. ⩽ . = 1, ... .. The interest in monosplines comes from their close relation with quadrature formulae.

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Multivariate Polynomial Interpolations Arising by Hyperplanes,given traces on the .-dimensional hyperplanes (0 ⩽ . ⩽ . - 1) which are intersections of some hyperplanes from .. We start with the case . = 0, i.e., pointwise interpolation with a node set arising by the hyperplanes ...

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