Interpolation by matrices
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منابع مشابه
THE USE OF SEMI INHERITED LU FACTORIZATION OF MATRICES IN INTERPOLATION OF DATA
The polynomial interpolation in one dimensional space R is an important method to approximate the functions. The Lagrange and Newton methods are two well known types of interpolations. In this work, we describe the semi inherited interpolation for approximating the values of a function. In this case, the interpolation matrix has the semi inherited LU factorization.
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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 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...
متن کاملNew Bases for Polynomial-Based Spaces
Since it is well-known that the Vandermonde matrix is ill-conditioned, while the interpolation itself is not unstable in function space, this paper surveys the choices of other new bases. These bases are data-dependent and are categorized into discretely l2-orthonormal and continuously L2-orthonormal bases. The first one construct a unitary Gramian matrix in the space l2(X) while the late...
متن کاملNumerical operations among rational matrices: standard techniques and interpolation
Numerical operations on and among rational matrices are traditionally handled by direct manipulation with their scalar entries. A new numerically attractive alternative is proposed here that is based on rational matrix interpolation. The procedure begins with evaluation of rational matrices in several complex points. Then all the required operations are performed consecutively on constant matri...
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تاریخ انتشار 2017