Inverse of a QT matrix

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The command inv returns the inverse of a QT matrix, represented in the QT format. To compute the inverse, it is necessary that the symbol $a(z)$ defining the Toeplitz part needs to be invertible, i.e., it needs to never vanish over the unit circle.

Contents

Syntax

Example

We choose a well-conditioned Toeplitz matrix, that can be inverted easily.

A = cqt([ 3 1 ], [ 3  1 ]);
iA = inv(A);
cqtinfo(iA)

 CQT matrix of size Inf x Inf
  - Rank of the correction: 1
  - Length of positive / negative symbol: 28 / 28

We can then test the accuracy of the computed inverse by testing that the inverse times the original matrix is close to the identity; we expect this number to be close to the truncatio threshold, that can be set with the cqtoption command.

res = norm( A * iA - eye(size(A), 'like', cqt), 'cqt')

res =

   1.2064e-11