# Newton Type Operator Interpolation Formulas Based on Interpolation by Means of Rational Functions

## Related Articles

- FINDING POLYNOMIAL PATTERNS AND NEWTON INTERPOLATION. Yajun Yang; Gordon, Sheldon P. // Mathematics & Computer Education;Spring2014, Vol. 48 Issue 2, p178
The article focuses on interpolation in the Newton interpolating formula for precalculus mathematics. Topics discussed include identification of polynomial pattern, substitution or elimination method in solving for unknown coefficients of a quadratic function and the sequential method in the...

- High Order Derivative Rational Interpolation Algorithm With Heredity. JING Ke; LIU Ye-zheng; KANG Ning // Applied Mathematics & Mechanics (1000-0887);Aug2014, Vol. 35 Issue 8, p87
Oscillatory rational interpolation was an important theme of function approximation, meanwhile, reducing the degree and solving the existence of the oscillatory rational interpolation function made a crucial problem for rational interpolation. The previous algorithms of osculatory rational...

- A New Approach to General Interpolation Formulae for Bivariate Interpolation. Le Zou; Shuo Tang // Abstract & Applied Analysis;2014, p1
General interpolation formulae for bivariate interpolation are established by introducing multiple parameters, which are extensions and improvements of those studied by Tan and Fang. The general interpolation formulae include general interpolation formulae of symmetric branched continued...

- A New Algorithm to Approximate Bivariate Matrix Function via Newton-Thiele Type Formula. Rongrong Cui; Chuanqing Gu // Journal of Applied Mathematics;2013, p1
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 formmotivated by Tan and Fang (2000), which is combined by...

- DERIVING SIMPSON'S RULE USING NEWTON INTERPOLATION. Gordon, Sheldon P.; Yajun Yang // Mathematics & Computer Education;Winter2016, Vol. 50 Issue 1, p34
The article discusses the derivation of Simpson's rule, which is a method for numerical integration, using Newton interpolation. Topics covered include the use of the Lagrange interpolation formula, emphasis on Newton's forward difference interpolating formula, and Simpson's 3/8 rule based on a...

- 100.14 Optimum choice of interpolation points in Newton's divided difference formula. McNAMEE, JOHN M. // Mathematical Gazette;Mar2016, Vol. 100 Issue 547, p143
The article presents mathematical formulas to prove the Newton's divided difference interpolation formula.

- Integral Newton-Type Polynomials with Continual Nodes. Makarov, V. L.; Khlobystov, V. V.; Kashpur, E. F.; Mikhal'chuk, B. R. // Ukrainian Mathematical Journal;Jun2003, Vol. 55 Issue 6, p942
We construct an integral Newton-type interpolation polynomial with a continual set of nodes. This interpolant is unique and preserves an operator polynomial of the corresponding degree.

- BLOCK BASED NEWTON-LIKE BLENDING INTERPOLATION. Qian-Jin Zhao; Jie-Qing Tan // Journal of Computational Mathematics;Jul2006, Vol. 24 Issue 4, p515
Newton's polynomial interpolation may be the favourite linear interpolation in the sense that it is built up by means of the divided differences which can be calculated recursively and produce useful intermediate results. However Newton interpolation is in fact point based interpolation since a...

- ON THE GENERALIZED INVERSE NEVILLE-TYPE MATRIX-VALUED RATIONAL INTERPOLANTS*. Zhibing Chen // Journal of Computational Mathematics;Mar2003, Vol. 21 Issue 2, p157
A new kind of matrix-valued rational interpolants is recursively established by means of generalized Samelson inverse for matrices, with scalar numerator and matrix-valued denominator. In this respect, it is essentially different from that of the previous works [7, 9], where the matrix-valued...

- A Computer-Based Barycentric Hermite Interpolation Optimization Algorithm Based on Lebesgue Constant Minimizing. Qianjin Zhao; Jie Qiao; Xianwen Fang // International Review on Computers & Software;Sep2012, Vol. 7 Issue 5, p2534
The most stable formula for a rational Hermite interpolation is the barycentric interpolation. The core problem is to choose the optimal weights. In this paper, we focus on the barycentric rational Hermite interpolation optimization algorithm. The optimal weights are obtained based on the...