timedom.norms {freqdom}

Compute operator norms of elements of a filter

Description

This function determines the norms of the matrices defining some linear filter.

Usage

timedom.norms(A, type = "2")

Arguments

A

an object of class timedom

type

matrix norm to be used as in norm

Details

Computes \|A_h\| for h in the set of lags belonging to the object A. When type is 2 then \|A\| is the spectral radius of A. When type is F then \|A\| is the Frobenius norm (or the Hilbert-Schmidt norm, or Schatten 2-norm) of A. Same options as for the function norm as in base package.

Value

A list which contains the following components:

• lags \quad a vector containing the lags of A.

• norms \quad a vector containing the norms of the matrices defining A.

Examples

d = 2

A = array(0,c(d,d,2))
A[1,,] = 2 * diag(d:1)/d
A[2,,] = 1.5 * diag(d:1)/d
OP = timedom(A,c(-2,1))
timedom.norms(OP)