Htykuut

I have been trying to understand the Wavelet transform in order to use it as a precondioner for ill-conditioned linear problems of the form $Avec{x}=vec{b}$.

I have come across this paper that is attempting to do the aforementioned. The paper lays out an algorithm in which I must compute $tilde{A} = RAR^T$ where $R$ is defined as:$$
D = begin{bmatrix}H_0^N \ H_1^Nend{bmatrix} ⊗ begin{bmatrix}H_0^N \ H_1^Nend{bmatrix}, quad R = begin{bmatrix}(G_0^N)^T \ (G_1^N)^Tend{bmatrix}^T ⊗ begin{bmatrix}(G_0^N)^T \ (G_1^N)^Tend{bmatrix}^T,
$$
where in turn $H$ and $G$ are defined as:begin{gather*}
H_i^{frac{N}{2^m}} ≜ {smallbegin{bmatrix}
h_i[0] & h_i[frac{N}{2^m} - 1] & h_i[frac{N}{2^m} - 2] & h_i[frac{N}{2^m} - 3] & cdots & cdots & h_i[2] & h_i[1]\
h_i[2] & h_i[1] & h_i[0] & h_i[frac{N}{2^m} - 1] & cdots & cdots & h_i[4] & h_i[3]\
h_i[4] & h_i[3] & h_i[2] & h_i[1] & cdots & cdots & h_i[6] & h_i[5]\
vdots & vdots & vdots & vdots & vdots & vdots & vdots & vdots\
vdots & vdots & vdots & vdots & vdots & vdots & vdots & vdots\
h[frac{N}{2^m} - 2] & h[frac{N}{2^m} - 3] & h[frac{N}{2^m} - 4] & h[frac{N}{2^m} - 5] & cdots & cdots & h_i[0] & h[frac{N}{2^m} - 1]
end{bmatrix}},\
G_i^{frac{N}{2^m}} ≜ {smallbegin{bmatrix}
g_i[0] & g_i[1] & g_i[2] & g_i[3] & cdots & cdots & g_i[frac{N}{2^m} - 2] & g_i[frac{N}{2^m} - 1]\
g_i[frac{N}{2^m} - 2] & g_i[frac{N}{2^m} - 1] & g_i[0] & g_i[1] & cdots & cdots & g_i[frac{N}{2^m} - 4] & g_i[frac{N}{2^m} - 3]\
g_i[frac{N}{2^m} - 4] & g_i[frac{N}{2^m} - 3] & g_i[frac{N}{2^m} - 2] & g_i[frac{N}{2^m} - 1] & cdots & cdots & g_i[frac{N}{2^m} - 6] & g_i[frac{N}{2^m} - 5]\
vdots & vdots & vdots & vdots & vdots & vdots & vdots & vdots\
vdots & vdots & vdots & vdots & vdots & vdots & vdots & vdots\
g_i[2] & g_i[3] & g_i[4] & g_i[5] & cdots & cdots & g_i[0] & g_i[1]
end{bmatrix}^T}.
end{gather*}

My question is: how do I calculate $R$ in MATLAB in order to compute $tilde{A} = RAR^{T}$? Is there a predefined function? I understand that MATLAB has dwt and dwt2, but these functions provide me with the results and not the matrix $R$.