Abstract Let f be analytic in the unit disk $${\mathbb {D}}=\{z\in {\mathbb {C}}:|z|&lt;1 \}$$ D = { z ∈ C : | &lt; 1 } </mml:mat...

In this paper, we investigate the complexity of the numerical construction of the Hankel structured low-rank approximation (HSLRA) problem, and develop a family of algorithms to solve this problem. Briefly, HSLRA is the problem of finding the closest (in some pre-defined norm) rank r approximation of a given Hankel matrix, which is also of Hankel structure. Unlike many other methods described i...

Hankel matrices are an important family of matrices that play a fundamental role in diverse fields of study, such as computer science, engineering, mathematics and statistics. In this paper, we study the behavior of the singular values of the Hankel matrix by changing its dimension. In addition, as an application, we use the obtained results for choosing the optimal values of the parameters of ...

The Hankel transform of a function by means of a direct Mellin approach requires sampling on an exponential grid, which has the disadvantage of coarsely undersampling the tail of the function. A novel modified Hankel transform procedure, not requiring exponential sampling, is presented. The algorithm proceeds via a three-step Mellin approach to yield a decomposition of the Hankel transform into...

Coding theory has played a central role in the development of computer science. One critical point of interaction is decoding error-correcting codes. First-and second-order Reed-Muller (RM(1) and RM(2), respectively) codes are two fundamental error-correcting codes which arise in communication as well as in probabilistically-checkable proofs and learning. In this paper, we take the first steps ...

This paper presents Levinson-type algorithms for (i) polynomial fitting, (ii) obtaining a Q decomposition of Vandermonde matrices and a Cholesky factorization of Hankel matrices and (iii) obtaining the inverse of Hankel matrices. The algorithm for the least-squares solution of Hankel systems of equations, requires 3n + 9n+ 3 multiply and divide operation (MD0). The algorithm for obtaining an or...

The completion of matrices with missing values under the rank constraint is a non-convex optimization problem. A popular convex relaxation is based on minimization of the nuclear norm (sum of singular values) of the matrix. For this relaxation, an important question is whether the two optimization problems lead to the same solution. This question was addressed in the literature mostly in the ca...