scholarly journals On the best choice of nodes at interpolation of functions by even Hermitian splines

2021 ◽  
pp. 25
Author(s):  
A.D. Malysheva
Keyword(s):  
Interpolation Of Functions

We have found exact values of deviation of even Hermitian splines on some classes of functions and pointed out the best choice of nodes at approximation of concrete functions by these splines.

Interpolation of functions in the Brillouin zone and special-point method

1983 ◽  
Vol 26 (5) ◽  
pp. 488-491
Author(s):  
M. L. Zolotarev ◽  
A. S. Poplavnoi
Keyword(s):  
Brillouin Zone ◽  
Point Method ◽  
Special Point ◽  
Interpolation Of Functions

Convex polyhedra in hyperbolic space and interpolation of functions

2011 ◽  
Vol 84 (3) ◽  
pp. 850-853
Author(s):  
O. P. Gladunova ◽  
E. D. Rodionov ◽  
V. V. Slavskii
Keyword(s):  
Hyperbolic Space ◽  
Convex Polyhedra ◽  
Interpolation Of Functions

scholarly journals Orthogonal structure on a quadratic curve

2020 ◽  
Author(s):  
Sheehan Olver ◽  
Yuan Xu
Keyword(s):  
Weight Function ◽  
Orthogonal Polynomials ◽  
Extension Problem ◽  
Orthogonal Expansions ◽  
Schrödinger’S Equation ◽  
Fourier Extension ◽  
Quadratic Curve ◽  
Interpolation Of Functions ◽  
Fourier Orthogonal Expansions ◽  
Schrödinger's Equation

Abstract Orthogonal polynomials on quadratic curves in the plane are studied. These include orthogonal polynomials on ellipses, parabolas, hyperbolas and two lines. For an integral with respect to an appropriate weight function defined on any quadratic curve, an explicit basis of orthogonal polynomials is constructed in terms of two families of orthogonal polynomials in one variable. Convergence of the Fourier orthogonal expansions is also studied in each case. We discuss applications to the Fourier extension problem, interpolation of functions with singularities or near singularities and the solution of Schrödinger’s equation with nondifferentiable or nearly nondifferentiable potentials.

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