MathTL::ApproximateUpFunction Class Reference

#include <up_function.h>

Inheritance diagram for MathTL::ApproximateUpFunction:

List of all members.

Public Member Functions
	ApproximateUpFunction (const unsigned int k)
double	value (const Point< 1, double > &p, const unsigned int component=0) const
void	vector_value (const Point< 1, double > &p, Vector< double > &values) const

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Detailed Description

It is well-known that the sequence of functions

u_0(x) = {[-1,1)}(x) u_{k+1}(x) = Lu_k(x), k=0,1,2,...

with the operator

Lf(x) = 2*int_{-}^x (f(2*t+1)-f(2*t-1)) dt = int_{-}^{2*x} (f(t+1)-f(t-1)) dt

converges to a fixed point of L which is a C^ function up(x) on [-1,1]. By definition, u_k is a spline of order k+1 with nodes at the dyadic points -1, -1+2^{-k+1}, -1+2*2^{-k+1},..., 1

The following class provides a function object for u_k.

References: Rvachev, "Compactly supported solutions of functional-differential equations", Russ. Math. Surv. 45 No. 1 (1990), 87-120

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The documentation for this class was generated from the following files:

• numerics/up_function.h
• numerics/up_function.cpp