romberg_alg: Romberg integration

In FREG: Functional Regression Models

Romberg integration

Description

Romberg integration is a process of numerical integration. Composite Trapezoidal Rule is used for the approximation of an integral. Then, Richardson extrapolation is used in order to improve previously computed approximations. The range over which the integral is defined is the range in which functional data are defined. When the relative error is infinitesimally small, convergence criterion is fulfilled.

Usage

romberg_alg(xbasis, bbasis)

Arguments

xbasis	basis functional data object used to represent functional covariate X. If covariate is a scalar variable, xbasis is a constant basis functional data object
bbasis	basis functional data object used to represent beta regression coefficient function for each independent variable

Value

S matrix

a matrix of inner product of two basis objects. The dimensions of the matrix are determined by the number of basis functions. The number of rows is equal to the number of basis functions for X, and the number of columns is equal to the number of basis functions for beta regression coefficient functions.

FREG documentation built on May 9, 2022, 5:07 p.m.