On a Particular 2-Periodic Lacunary Trigonometric Interpolation Problem on Equidistant Nodes

1989 ◽  
Vol 16 (3-4) ◽  
pp. 383-404 ◽  
Author(s):  
A. Sharma ◽  
R.S. Varga
Keyword(s):  
Interpolation Problem ◽  
Trigonometric Interpolation ◽  
Equidistant Nodes

scholarly journals Trigonometric interpolation

1992 ◽  
Vol 35 (3) ◽  
pp. 457-472
Author(s):  
T. N. T. Goodman ◽  
A. Sharma
Keyword(s):  
Interpolation Problem ◽  
Arbitrary Sequence ◽  
Trigonometric Interpolation ◽  
Equidistant Nodes ◽  
Explicit Expressions

We consider interpolation at 2n equidistant nodes in [0,π) from the space ℱN spanned by sines and cosines of odd multiples of x. This interpolation problem is shown to be correct for an arbitrary sequence of derivatives specified at all the nodes. Explicit expressions for the fundamental polynomials are obtained and it is shown that under mild smoothness assumptions on the function f interpolant from ℱN converges uniformly to f as the node spacing goes to zero.

SOME 2-PERIODIC TRIGONOMETRIC INTERPOLATION PROBLEMS ON EQUIDISTANT NODES

Analysis ◽  
1991 ◽  
Vol 11 (2-3) ◽  
Author(s):  
A. SHARMA ◽  
J . SZABADOS ◽  
R . S . VARGA
Keyword(s):  
Trigonometric Interpolation ◽  
Interpolation Problems ◽  
Equidistant Nodes

LACUNARY TRIGONOMETRIC INTERPOLATION ON EQUIDISTANT NODES

Analysis ◽  
1986 ◽  
Vol 6 (2-3) ◽  
Author(s):  
A. Jakimovski ◽  
A. Sharma
Keyword(s):  
Trigonometric Interpolation ◽  
Equidistant Nodes

Convergence of lacunary trigonometric interpolation on equidistant nodes

1982 ◽  
Vol 39 (1-3) ◽  
pp. 27-37 ◽  
Author(s):  
S. Riemenschneider ◽  
A. Sharma ◽  
P. W. Smith
Keyword(s):  
Trigonometric Interpolation ◽  
Equidistant Nodes

scholarly journals Lidstone–Euler Second-Type Boundary Value Problems: Theoretical and Computational Tools

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Francesco Aldo Costabile ◽  
Maria Italia Gualtieri ◽  
Anna Napoli
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Interpolation Problem ◽  
Boundary Value ◽  
Computational Tools ◽  
Numerical Examples ◽  
Odd Order ◽  
Uniqueness Of The Solution ◽  
Type Boundary

AbstractGeneral nonlinear high odd-order differential equations with Lidstone–Euler boundary conditions of second type are treated both theoretically and computationally. First, the associated interpolation problem is considered. Then, a theorem of existence and uniqueness of the solution to the Lidstone–Euler second-type boundary value problem is given. Finally, for a numerical solution, two different approaches are illustrated and some numerical examples are included to demonstrate the validity and applicability of the proposed algorithms.

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