The complex optimal step-size for Tensor Decomp.

New ALS methods with extrapolating search directions and optimal step size

In signal processing, data analysis and scientific computing, one often encounters the problem of decomposing a tensor into a sum of contributions. To solve such problems, both the search direction and the step size are two crucial elements in numerical algorithms, such as alternating least squares algorithm (ALS).

This is an ALS with line-search methods for third-order tensor decompositions. The novel technique here is the subroutine of the direct method for computing the complex optimal step-size (OSSc). A heuristic implementation of this direct method (OSSs) is often fast than the optimal step-size. Two extrapolating search-directions, geometric and algebraic ("geo" and "alg"), are more efficient than the linear direction.

Enjoy!