This paper proposes a direct solver for symmetric indefinite linear systems. The program is parallelized via the OpenMP task construct and outperforms existing programs. proposed avoids pivoting, which requires lot of data movement, during factorization with preconditioning using random butterfly transformation. matrix layout tiled after to more efficiently use cache memory factorization. Given...

Consider three normal operators A,B,C on a separable Hilbert space ? as well scalar-valued spectral measures ? A ?(A), B ?(B) and C ?(C). For any ??L ? (? ×? ) X,Y?S 2 (?), the of Hilbert–Schmidt ?, we provide general definition triple operator integral ? (?)(X,Y) belonging to S (?) in such way that (?) belongs (S (?)×S (?),S (?)) bounded bilinear resulting mapping :L )?B is w * -continuous iso...

Inheritance hierarchies often constitute the backbone of object-oriented systems. Their quality is therefore quite crucial. We present here our work the objective of which is to help designers to improve and to measure the quality of their inheritance hierarchies. The quality we deal with is the degree of factorization of information. Our work is based on the mathematical structure of Galois (c...

We construct a 1-factorization of the complement Σm of the linear Hamming code of length m = mr = 2 r − 1 in the m-cube Qm, for r ≥ 2, having the following equitable property: its component 1-factors intersect each Cayley parallel 1-factor of Qm at a constant number of edges, (namely 2r edges). In the way to that construction, we find an equitable mr−1-factorization of Σm formed by two factors ...

For a number of computational search problems the existence of a polynomial time algorithm for the problem implies that a polynomial time algorithm for the problem is constructively known Some instances of such self witnessing polynomial time complexity are presented Our main result demonstrates this property for the problem of computing the prime factorization of a positive integer based on a ...

We consider three notions of factorization arising in different frameworks: factorizing languages, factorization of the natural numbers, factorizing codes. A language X ⊆ A∗ is called factorizing if there exists a language Y ⊆ A∗ such that XY = A∗ and the product is unambiguous. This is a decidable property for recognizable languages X . If we consider the particular case of unary alphabets, we...

This paper proposes, analyzes, and numerically tests methods to assure the existence of incomplete Cholesky (IC) factorization preconditioners, based solely on the target sparsity pattern for the triangular factor R. If the sparsity pattern has a simple property (called property C+), then the IC factor exists in exact arithmetic. Two algorithms for modifying the target sparsity pattern to have ...

Non-negative matrix factorization ( NMF ) is a new knowledge discovery method that is used for text mining, signal processing, bioinformatics, and consumer analysis. However, its basic property as a learning machine is not yet clarified, as it is not a regular statistical model, resulting that theoretical optimization method of NMF has not yet established. In this paper, we study the real log c...

The purpose of this note is to understand the two out of three property of the model category in terms of the weak factorization systems. We will show that if a category with classes of trivial cofibrations, cofibrations, trivial fibrations, and fibrations is given a simplicial structure similar to that of the simplicial model category, then the full subcategory of cofibrant and fibrant objects...

In this paper we study the complexity of factorization of polynomials in the free noncommutative ring F〈x1, x2, . . . , xn〉 of polynomials over the field F and noncommuting variables x1, x2, . . . , xn. Our main results are the following: • Although F〈x1, . . . , xn〉 is not a unique factorization ring, we note that variabledisjoint factorization in F〈x1, . . . , xn〉 has the uniqueness property....