Given a symmetric positive definite matrix A, we compute a structured approximate Cholesky factorization A ≈ RTR up to any desired accuracy, where R is an upper triangular hierarchically semiseparable (HSS) matrix. The factorization is stable, robust, and efficient. The method compresses off-diagonal blocks with rank-revealing orthogonal decompositions. In the meantime, positive semidefinite te...

The factorization property of graviton scattering amplitudes is reviewed and shown to be valid only if the “natural” value of the gyromagnetic ratio gS = 2 is employed—independent of spin.

We continue investigating the superintegrability property of matrix models, i.e. factorization model averages characters. This paper focuses on Gaussian Hermitian example, where role characters is played by Schur functions. find a new intriguing corollary superintegrability: an infinite set correlators bilinear in More exactly, these are products functions and polynomials $K_\Delta$ that form c...

Nonnegative Matrix Factorization (NMF) algorithms have been utilized in a wide range of real applications. NMF is done by several researchers to its part based representation property especially in the facial expression recognition problem. It decomposes a face image into its essential parts (e.g. nose, lips, etc.) but in all previous attempts, it is neglected that all features achieved by NMF ...

A ring R is called strongly clean if every element of R is the sum of a unit and an idempotent that commute. By SRC factorization, Borooah, Diesl, and Dorsey [3] completely determined when Mn(R) over a commutative local ring R is strongly clean. We generalize the notion of SRC factorization to commutative rings, prove that commutative n-SRC rings (n ≥ 2) are precisely the commutative local ring...

Algorithms for the solution of symmetric diagonally dominant tridiagonal systems of linear equations with constant diagonals are considered. Such systems occur, for example, when solving certain constant-coecient elliptic partial diierential equations by the Fourier method. In particular, the specialized LU factorization method of Malcolm and Palmer (SpLU), the cyclic reduction method of Hockne...

We study the relation (and differences) between stability and Property (S) in simple stably finite framework. This leads us to characterize stable elements terms of their support, these concepts from different sides: hereditary subalgebras, projections multiplier algebra order properties Cuntz semigroup. use approaches show both that cancellation at infinity on semigroup just holds when its equ...

Abstract In this article, we evaluate determinants of “block hook” matrices, which are block matrices consist hook matrices. particular, deduce that the determinant a matrix factorizes nicely. addition give combinatorial interpretation aforesaid factorization property by counting weighted paths in suitable digraph.