In this paper, we investigate the problem of real-time polyphonic music transcription by employing non-negative matrix factorization techniques and the β-divergence as a cost function. We consider real-world setups where the music signal arrives incrementally to the system and is transcribed as it unfolds in time. The proposed transcription system is addressed with a modified non-negative matri...

In this paper‎, ‎an efficient dropping criterion has been used to compute the IUL factorization obtained from Backward Factored APproximate INVerse (BFAPINV) and ILU factorization obtained from Forward Factored APproximate INVerse (FFAPINV) algorithms‎. ‎We use different drop tolerance parameters to compute the preconditioners‎. ‎To study the effect of such a dropping on the quality of the ILU ...

The paper concerns the problem of decomposition of a large-scale linear dynamic system into two subsystems. An equivalent problem is to split the characteristic polynomial of the original system into two polynomials of lower degrees. Conditions are found concerning the coefficients of the original polynomial which must be fulfilled for its factorization. It is proved that knowledge of only one ...

An optical system to execute prime factorization is modified to improve its processing performance. In the improvement, some deletions in interference measurements are permitted. As results, it is experimentally verified that the improved method can provide correct results in factorization of 30bits integer.

The problem of expressing a given nonlinear statespace system as the cascade connection of a lossless system and a stable, minimum-phase system (inner-outer factorization) is solved for the case of a stable system having state-space equations affine in the inputs. The solution is given in terms of the stabilizing solution of a certain Hamilton-Jacobi equation. The stable, minimum-phase factor i...

A multivariable model reference adaptive control system (MRACS) design method for a plant with m inputs and p outputs is proposed (m # p). Using an interactor matrix the coprime factorization of the plant for (1) m > p case, and (2) m < p case is derived. Further, using this coprime factorization the structure of MRACS is established.

It is well-known that a factorization system on a category (with sufficient pullbacks) gives rise to a fibration. This paper characterizes the fibrations that arise in such a way, by making precise the logical structure that is given by factorization systems. The underlying motivation is to obtain general Birkhoff results in a fibred setting.

We have developed a highly parallel sparse Cholesky factorization algorithm that substantially improves the state of the art in parallel direct solution of sparse linear systems—both in terms of scalability and overall performance. It is a well known fact that dense matrix factorization scales well and can be implemented efficiently on parallel computers. However, it had been a challenge to dev...