Correction extraction

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QT matrices are defined as $A = T(a(z)) + E_a$, where $E_a$ is a compact correction approximated by a low-rank matrix with finite support.

This correction can be extracted, either as a full matrix or in factored form (the latter is usually much better from the efficiency viewpoint).

The symbol can be accessed using the symbol command.

Contents

Syntax

Example

A simple way to generate matrices with a correction is taking the inverse of a Toeplitz matrix which is not triangular.

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

The correction can be extracted in full form

EA = correction(iA);
support = size(EA)
EA(1:4, 1:4)

support =

    27    26


ans =

   -0.0652    0.0249   -0.0095    0.0036
    0.0249   -0.0095    0.0036   -0.0014
   -0.0095    0.0036   -0.0014    0.0005
    0.0036   -0.0014    0.0005   -0.0002

... or in factored form, which requires much less storage (notice how in this case the correction has rank equal to $1$).

[UA, VA] = correction(iA);
supportU = size(UA)
supportV = size(VA)

supportU =

    27     1


supportV =

    26     1