ifsm.setQF: Sets up the quadratic form for the IFSM

In ifs: Iterated Function Systems

Sets up the quadratic form for the IFSM

Description

Tool function to construct the quadratic form x'Qx + b'x + l2 to be minimized under some constraint depending on l1. This is used to construct the IFSM operator.

Usage

ifsm.setQF(u, s, a)

Arguments

u	the vector of values of the target function u
s	the vector of coefficients s_i in: w_i = s_i *x + a_i
a	the vector of coefficients a_i in: w_i = s_i *x + a_i

Details

This operator is intended to approximate a function on L2[0,1]. If ‘u’ is simulated, then the IFSM can be used to simulate a IFSM version of ‘u’.

Value

List of elements

Q	the matrix of the quadratic form
b	the matrix of the quadratic form
L1	the L1 norm of the target function
L2	the L2 norm of the target function
M1	the integral of the target function

Author(s)

S. M. Iacus

References

Iacus, S.M, La Torre, D. (2005) IFSM representation of Brownian motion with applications to simulation, forthcoming.

See Also

IFSM

ifs documentation built on Sept. 9, 2022, 3:09 p.m.