A 0-1 matrix has the Consecutive Ones Property (C1P) if there is a permutation of its columns that leaves the 1’s consecutive in each row. The Consecutive Ones Submatrix (COS) problem is, given a 0-1 matrix A, to find the largest number of columns of A that form a submatrix with the C1P property. Such a problem has potential applications in physical mapping with hybridization data. This paper p...

The sparse matrix-vector multiplication (SpMxV) is a kernel operation widely used in iterative linear solvers. The same sparse matrix is multiplied by a dense vector repeatedly in these solvers. Matrices with irregular sparsity patterns make it difficult to utilize cache locality effectively in SpMxV computations. In this work, we investigate singleand multiple-SpMxV frameworks for exploiting c...

Necessary and sufficient conditions are given for a substochastic semigroup on L obtained through the Kato–Voigt perturbation theorem to be either stochastic or strongly stable. We show how such semigroups are related to piecewise deterministic Markov process, provide a probabilistic interpretation of our results, and apply them to fragmentation equations.

This work introduces new relative perturbation bounds for the LDU factorization of (row) diagonally dominant matrices under structure-preserving componentwise perturbations. These bounds establish that if (row) diagonally dominant matrices are parameterized via their diagonally dominant parts and off-diagonal entries, then tiny relative componentwise perturbations of these parameters produce ti...

The sparse matrix-vector multiplication (SpMxV) is a kernel operation widely used in iterative linear solvers. The same sparse matrix is multiplied by a dense vector repeatedly in these solvers. Matrices with irregular sparsity patterns make it difficult to utilize cache locality effectively in SpMxV computations. In this work, we investigate singleand multiple-SpMxV frameworks for exploiting c...

The sparse matrix-vector multiplication (SpMxV) is a kernel operation widely used in iterative linear solvers. The same sparse matrix is multiplied by a dense vector repeatedly in these solvers. Matrices with irregular sparsity patterns make it difficult to utilize cache locality effectively in SpMxV computations. In this work, we investigate singleand multiple-SpMxV frameworks for exploiting c...

We investigate (0,1)-matrices that are convex, which means the ones consecutive in every row and column. These matrices occur discrete tomography. The notion of ranked essential sets, known for permutation matrices, is extended to convex sets. show a number results class C(R,S) with given column sum vectors R S. Also, it shown set uniquely determines matrix C(R,S).

Kipadia, Nirav Harish. M.S.E.E., Purdue University. May 1994. Pi SIMD Sparse Matrix-Vector Multiplication Algorithm for Computational Electromagnetics and Scattering Matrix Models. Major Professor: Jose Fortes. A large number of problems in numerical analysis require the multiplication of a sparse matrix by a vector. In spite of the large amount of fine-grained parallelism available in the proc...

We investigate alternating sign matrices that are not permutation matrices, but have finite order in a general linear group. classify all such examples of the form P + T , where is matrix and has four non-zero entries, forming square with entries 1 −1 each row column. show multiplicative orders these do always coincide those same size. pose problem identifying subgroups groups generated by matr...

A new format for storing sparse matrices is proposed for efficient sparse matrix-vector (SpMV) product calculation on modern throughput-oriented computer architectures. This format extends the standard compressed row storage (CRS) format and is easily convertible to and from it without any memory overhead. Computational performance of an SpMV kernel for the new format is determined for over 140...