scholarly journals Optimal Error Bounds for Quadratic Spline Interpolation

1996 ◽  
Vol 198 (1) ◽  
pp. 49-63 ◽  
Author(s):  
François Dubeau ◽  
Jean Savoie
Keyword(s):  
Error Bounds ◽  
Spline Interpolation ◽  
Optimal Error ◽  
Quadratic Spline

Quadratic spline interpolation on uniform meshes

1990 ◽  
Vol 30 (3) ◽  
pp. 484-489 ◽  
Author(s):  
M. N. El Tarazi
Keyword(s):  
Spline Interpolation ◽  
Quadratic Spline

scholarly journals Error Analysis for a Noisy Lacunary Cubic Spline Interpolation and a Simple Noisy Cubic Spline Quasi Interpolation

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Feng-Gong Lang ◽  
Xiao-Ping Xu
Keyword(s):  
Error Analysis ◽  
Error Bounds ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Cubic Spline ◽  
The Other ◽  
Cubic Spline Interpolation ◽  
Numerical Tests ◽  
New Methods ◽  
Noisy Function

We mainly present the error analysis for two new cubic spline based methods; one is a lacunary interpolation method and the other is a very simple quasi interpolation method. The new methods are able to reconstruct a function and its first two derivatives from noisy function data. The explicit error bounds for the methods are given and proved. Numerical tests and comparisons are performed. Numerical results verify the efficiency of our methods.

scholarly journals Revisited Optimal Error Bounds for Interpolatory Integration Rules

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
François Dubeau
Keyword(s):  
Error Bounds ◽  
Error Term ◽  
Quadrature Rules ◽  
Optimal Error ◽  
Integration By Parts ◽  
Integration Rules

We present a unified way to obtain optimal error bounds for general interpolatory integration rules. The method is based on the Peano form of the error term when we use Taylor’s expansion. These bounds depend on the regularity of the integrand. The method of integration by parts “backwards” to obtain bounds is also discussed. The analysis includes quadrature rules with nodes outside the interval of integration. Best error bounds for composite integration rules are also obtained. Some consequences of symmetry are discussed.

scholarly journals Optimal error bounds for two-grid schemes applied to the Navier–Stokes equations

2012 ◽  
Vol 218 (13) ◽  
pp. 7034-7051 ◽  
Author(s):  
Javier de Frutos ◽  
Bosco García-Archilla ◽  
Julia Novo
Keyword(s):  
Error Bounds ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Optimal Error ◽  
Navier Stokes Equations

C2 Rational Quadratic Spline Interpolation to Monotonic Data

1983 ◽  
Vol 3 (2) ◽  
pp. 141-152 ◽  
Author(s):  
R. DELBOURGO ◽  
J. A. GREGORY
Keyword(s):  
Spline Interpolation ◽  
Quadratic Spline
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