The accurate solution of some of the main problems in numerical linear algebra (linear system solving, eigenvalue computation, singular value computation and the least squares problem) for a totally positive Bernstein–Vandermonde matrix is considered. Bernstein–Vandermonde matrices are a generalization of Vandermonde matrices arising when considering for the space of the algebraic polynomials o...

We design a grid based multilevel incomplete LU preconditioner (GILUM) for solving general sparse matrices. This preconditioner combines a high accuracy ILU factorization with an algebraic multilevel recursive reduction. The GILUM precondi-tioner is a compliment to the domain based multilevel block ILUT preconditioner. A major diierence between these two preconditioners is the way that the coar...

Algebraic factorization is an extremely important part of any logic synthesis system but is computationally expensive. Hence it is important to look at parallel processing to speed up the procedure. This paper presents three different parallel algorithms for algebraic factorization. The first algorithm uses circuit replication and uses a divide and conquer strategy. A second algorithm uses tota...

This paper proposes a hierarchical probabilistic model for ordinal matrix factorization. Unlike previous approaches, we model the ordinal nature of the data and take a principled approach to incorporating priors for the hidden variables. Two algorithms are presented for inference, one based on Gibbs sampling and one based on variational Bayes. Importantly, these algorithms may be implemented in...

The problem of binary factorization of complex patterns in recurrent Hopfieldlike neural network was studied both theoretically and by means of computer simulation. The number and sparseness of factors mixed in patterns crucially determines the ability of an autoassociator to perform a factorization. Basing on experimental data on memory and learning one may suggest, that there exists a neural ...

The traditional subspace-based approaches to segmentation (often referred to as multi-body factorization approaches) provide spatial clustering/segmentation by grouping together points moving with consistent motions. We are exploring a dual approach to factorization, i.e., obtaining temporal clustering/segmentation by grouping together frames capturing consistent shapes. Temporal cuts are thus ...

This paper discusses the core factorization routines included in the ScaLAPACK library. These routines allow the factorization and solution of a dense system of linear equations via LU, QR, and Cholesky. They are implemented using a block cyclic data distribution, and are built using de facto standard kernels for matrix and vector operations (BLAS and its parallel counterpart PBLAS) and message...

Standard (single-level) incomplete factorization preconditioners are known to successfully accelerate Krylov subspace iterations for many linear systems. The classical Modified Incomplete LU (MILU) factorization approach improves the acceleration given by (standard) ILU approaches, by modifying the non-unit diagonal in the factorization to match the action of the system matrix on a given vector...

Nonnegative Matrix Factorization (NMF) is a technique to approximate a nonnegative matrix as a product of two smaller nonnegative matrices. The guaranteed nonnegativity of the factors allows interpreting the approximation as an additive combination of features, a distinctive property that other widely used matrix factorization methods do not have. Several advanced methods for computing this fac...

Recommender system plays an important role in our daily life. Recommender systems naturally intimate items to users that might be fascinating for them. We propose probabilistic matrix factorization technique for recommendations. The (PMF) model is proposed which computes continuously with the number of investigations and, more specially, functions well on the massive, inadequate, and very uneve...