منابع مشابه
Barycentric Lagrange Interpolation
Barycentric interpolation is a variant of Lagrange polynomial interpolation that is fast and stable. It deserves to be known as the standard method of polynomial interpolation.
متن کاملConstrained Interpolation via Cubic Hermite Splines
Introduction In industrial designing and manufacturing, it is often required to generate a smooth function approximating a given set of data which preserves certain shape properties of the data such as positivity, monotonicity, or convexity, that is, a smooth shape preserving approximation. It is assumed here that the data is sufficiently accurate to warrant interpolation, rather than least ...
متن کاملHermite Interpolation Outperforms Nyström Interpolation
Hermite interpolation is shown to be much more stable than Nyström interpolation in the context of solving classic Fredholm second kind integral equations of potential theory in two dimensions using panel-based Nyström discretization. AMS subject classification (2000): 31A10,45B05,65D05,65R20.
متن کاملStability of Barycentric Interpolation Formulas
The barycentric interpolation formula defines a stable algorithm for evaluation at points in [−1, 1] of polynomial interpolants through data on Chebyshev grids. Here it is shown that for evaluation at points in the complex plane outside [−1, 1], the algorithm becomes unstable and should be replaced by the alternative modified Lagrange or “first barycentric” formula dating to Jacobi in 1825. Thi...
متن کاملQuantum Hermite Interpolation Polynomials
Abstract. The concept of Lagrange and Hermite interpolation polynomials can be generalized. The spectral basis of idempotents and nilpotents of a factor ring of polynomials provides a powerful framework for the expression of Lagrange and Hermite interpolation in 1, 2 and higher dimensional spaces. We give a new definition of quantum Lagrange and Hermite interpolation polynomials which works on ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Scientific Computing
سال: 2013
ISSN: 1064-8275,1095-7197
DOI: 10.1137/110833221