rluce / tlcomp

Computing with Toeplitz and Toeplitz-like matrices in Matlab
MIT License
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Use ACA to approximate a given A with a TL matrix #1

Open rluce opened 7 years ago

rluce commented 7 years ago

Given a matrix A that is potentially close to a TL matrix, we would like to generate a TL matrix by

T = TLMat(A)

so that an efficient representation of A is obtained. This is currently achieved by computing its displacement D(A), and computing a SVD of D(A), which is expensive (cubic operation).

A more economic choice would be to use Adaptive Cross Approximation on D(A) to recover a low rank approximation (essentially d * n^2, where d is the rank). We then should also support syntax for controlling the rank, i.e.

T = TLMat(A, d) % prescribed drank d T = TLMat(A, tol) % prescribed tolerance pivot_k / pivot_1 that indicates to stop