Spline approximation with interpolation constraints for numerical integration

Abstract

By using a Walsh-type theorem, we impose a finite number of interpolation constraints to a polynomial spline approximation operator. These constrained approximating splines reproduce polynomials and give orders of convergence identical to those of the unconstrained ones. We give an application in numerical integration by using the constrained splines for evaluation of Cauchy principal value integrals.

Keywords:

• Approximating splines
• constrained approximating splines
• locally uniform partition
• Cauchy principal value integrals

ASM Subject classification:

• 65D05
• 65D07
• 65D30

C.R. Categories:

• G.1.4