The two-dimensional matrix of coefficients for the Laplacian operator is shown in (11), where, on a Cartesian space, h=0, and in the helix geometry, h=-1. (A similar partitioned matrix arises from packing a cylindrical surface into a array.) Notice that the partitioning becomes transparent for the helix, h=-1. With the partitioning thus invisible, the matrix simply represents one-dimensional convolution and we have an alternative analytical approach, one-dimensional Fourier Transform. We often need to solve sets of simultaneous equations with a matrix similar to (11). The method we use is triangular factorization.
Although the autocorrelation has mostly zero values, the factored autocorrelation from (8) has a great number of nonzero terms, but fortunately they seem to be converging rapidly (in the middle) so truncation (of the middle coefficients) seems reasonable. I wish I could show you a larger matrix, but all I can do is to pack the signal into shifted columns of a lower triangular matrix like this: