In this paper we consider two structure prediction problems of interest in Gaussian elimination with partial pivoting of sparse matrices. First, we consider the problem of determining the nonzero structure of the factors L and U during the factorization. We present an exact prediction of the structure, that identifies some numeric cancellations appearing during Gaussian elimination. The numeric...

Non-negative matrix factorization (NMF) is an unsupervised method whose aim is to find an approximate factorization Vn*m=Wn*r*Hr*m into non-negative matrices Wn*r and Hr*m. This paper presents an extension to NMF and discusses the development and the use of damped Newton based the non-negative matrix factorization called DNNMF with good convergence property for wood defects detection. We also p...

In a recent paper (Del Sol Mesa A and Quesne C 2000 J. Phys. A: Math. Gen. 33 4059), we started a systematic study of the connections among different factorization types, suggested by Infeld and Hull, and of their consequences for the construction of algebras. We devised a general procedure for constructing satellite algebras for all the Hamiltonians admitting a type E factorization by using th...

In the paper we derive and discuss a wide class of algorithms for 3D Super-symmetric nonnegative Tensor Factorization (SNTF) or nonnegative symmetric PARAFAC, and as a special case: Symmetric Nonnegative Matrix Factorization (SNMF) that have many potential applications, including multi-way clustering, feature extraction, multisensory or multi-dimensional data analysis, and nonnegative neural sp...

In a recent paper (Del Sol Mesa A and Quesne C 2000 J. Phys. A: Math. Gen. 33 4059), we started a systematic study of the connections among different factorization types, suggested by Infeld and Hull, and of their consequences for the construction of algebras. We devised a general procedure for constructing satellite algebras for all the Hamiltonians admitting a type E factorization by using th...

Nonnegative Matrix Factorization (NMF) is an efficient technique to approximate a large matrix containing only nonnegative elements as a product of two nonnegative matrices of significantly smaller size. The guaranteed nonnegativity of the factors is a distinctive property that other widely used matrix factorization methods do not have. Matrices can also be seen as second-order tensors. For som...

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...

Matrices coming from elliptic Partial Differential Equations have been shown to have a low4 rank property: well defined off-diagonal blocks of their Schur complements can be approximated by low-rank 5 products and this property can be efficiently exploited in multifrontal solvers to provide a substantial reduction 6 of their complexity. Among the possible low-rank formats, the Block Low-Rank fo...

In this paper, we consider a weakening of the definitions of uniform and perfect one-factorizations of the complete graph. Basically, we want to order the 2n − 1 one-factors of a one-factorization of the complete graph K2n in such a way that the union of any two (cyclically) consecutive one-factors is always isomorphic to the same two-regular graph. This property is termed sequentially uniform;...

Earlier we justified our proof of the fundamental theorem of arithmetic by arguing that the result was not obvious, since its analogue in the ring E of even integers did not hold. Here we will explore a far more exciting explanation: essentially the same proof can be used to show that certain other “integer-like rings” have the unique factorization property. The unique factorization property ca...