construct.K: Construct the K matrix for a given multivariate basis.

Description Usage Arguments Value

Description

This function constructs the K matrix for a given multivariate basis assuming the basis is a Legendre polynomial basis and the smoothing criterion is the Frobenius norm of the Hessian integrated over [-1, 1]^d.

Usage

1
construct.K(basis)

Arguments

basis

A matrix. Rows of the matrix are taken as the exponent vectors of the leading terms of a Legendre polynomial basis.

Value

A matrix where each entry is <f, g> with

<f, g> = \int_X ∑_{i,j}\frac{d^2f}{dx_idx_j}\frac{d^2g}{dx_idx_j} dx,

with f, g being the Legendre polynomials described by the appropriate exponent vectors.


peterrobertcurtis/SSM documentation built on May 25, 2019, 2:10 a.m.