A Method of Neville-like Vector-valued Blending Rational Interpolants Based on Continued Fractions

2014 ◽  
Vol 11 (8) ◽  
pp. 2647-2654
Author(s):  
Chunyan Duan
Keyword(s):  
Continued Fractions ◽  
Rational Interpolants ◽  
Vector Valued

Vector-valued, rational interpolants III

1986 ◽  
Vol 2 (1) ◽  
pp. 263-289 ◽  
Author(s):  
P. R. Graves-Morris ◽  
C. D. Jenkins
Keyword(s):  
Rational Interpolants ◽  
Vector Valued

scholarly journals Vector valued rational interpolants over triangular grids

2002 ◽  
Vol 44 (10-11) ◽  
pp. 1357-1367 ◽  
Author(s):  
Jieqing Tan ◽  
Baorui Song ◽  
Gongqin Zhu
Keyword(s):  
Triangular Grids ◽  
Rational Interpolants ◽  
Vector Valued

A New Approach to Trivariate Blending Rational Interpolation

2012 ◽  
Vol 546-547 ◽  
pp. 570-575 ◽  
Author(s):  
Le Zou ◽  
Jin Xie ◽  
Chang Wen Li
Keyword(s):  
Continued Fractions ◽  
Rational Interpolation ◽  
Interpolation Formula ◽  
Linear Interpolation ◽  
Interpolation Theorem ◽  
Newton Interpolation ◽  
New Approach ◽  
Barycentric Interpolation ◽  
Rational Interpolants ◽  
Data Pair

The advantages of barycentric interpolation formulations in computation are small number of floating points operations and good numerical stability. Adding a new data pair, the barycentric interpolation formula don’t require to renew computation of all basis functions. Thiele-type continued fractions interpolation and Newton interpolation may be the favoured nonlinear and linear interpolation. A new kind of trivariate blending rational interpolants were constructed by combining barycentric interpolation, Thiele continued fractions and Newton interpolation. We discussed the interpolation theorem, dual interpolation, no poles of the property and error estimation.

Clifford algebras and vector-valued rational forms. I

1990 ◽  
Vol 431 (1882) ◽  
pp. 285-300 ◽  
Keyword(s):  
Continued Fractions ◽  
Clifford Algebras ◽  
Recurrence Relations ◽  
Generalized Inverse ◽  
Multiplicative Group ◽  
Group Inverse ◽  
Scalar Theory ◽  
Real Analytic ◽  
Usual Scalar ◽  
Vector Valued

We demonstrate how Clifford algebras offer a framework for the construction of vector-valued rational forms possessing features of the usual scalar theory, including three-term recurrence relations for continued fractions. The price for this advantage is that the Moore–Penrose generalized inverse is replaced by the multiplicative group inverse of a Clifford algebra. However, the connection between the new vector-valued rational forms and generalized inverse rational forms is a close one; in fact, the two forms are identical for real analytic data.

scholarly journals A New Algorithm to Approximate Bivariate Matrix Function via Newton-Thiele Type Formula

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Rongrong Cui ◽  
Chuanqing Gu
Keyword(s):  
Continued Fractions ◽  
Matrix Function ◽  
Continued Fraction ◽  
Generalized Inverse ◽  
New Method ◽  
Rectangular Grid ◽  
Type Formula ◽  
The Matrix ◽  
Rational Interpolants ◽  
Better Than

A new method for computing the approximation of bivariate matrix function is introduced. It uses the construction of bivariate Newton-Thiele type matrix rational interpolants on a rectangular grid. The rational interpolant is of the form motivated by Tan and Fang (2000), which is combined by Newton interpolant and branched continued fractions, with scalar denominator. The matrix quotients are based on the generalized inverse for a matrix which is introduced by C. Gu the author of this paper, and it is effective in continued fraction interpolation. The algorithm and some other important conclusions such as divisibility and characterization are given. In the end, two examples are also given to show the effectiveness of the algorithm. The numerical results of the second example show that the algorithm of this paper is better than the method of Thieletype matrix-valued rational interpolant in Gu (1997).

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