freqdom (version 2.0.5)

timedom.norms: 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")

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.

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.

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)