Let S be a subset of diagonal entries of an n × n complex matrix A. When the members of S have a common value which is equal to an eigenvalue of A, then S is a critical diagonal set of A. The existence of such a set is equivalent to the matrix Ã, obtained from A by setting its diagonal entries equal to zero, having an s × t zero submatrix with s + t ≥ n + 1. If S is a minimal critical diagonal ...

New preconditioning strategies for solving m × n overdetermined large and sparse linear least squares problems using the CGLS method are described. First, direct preconditioning of the normal equations by the Balanced Incomplete Factorization (BIF) for symmetric and positive definite matrices is studied and a new breakdown-free strategy is proposed. Preconditioning based on the incomplete LU fa...

We present an optimal data structure for submatrix maximum queries in n×nMonge matrices. Our result is a two-way reduction showing that the problem is equivalent to the classical predecessor problem in a universe of polynomial size. This gives a data structure of O(n) space that answers submatrix maximum queries in O(log logn) time, as well as a matching lower bound, showing that O(log log n) q...

the realization optimality theory is a recent development in the original optimality theory which is proposed to deal with morphological issues especially the inflectional ones. its main idea is to consider the morphological realization rules as ranked violable language-specific constraints that control the realization processes and provide phonological information of grammatical morphemes. thi...

The sparse hypermatrix storage scheme produces a recursive 2D partitioning of a sparse matrix. Data subblocks are stored as dense matrices. Since we are dealing with sparse matrices some zeros can be stored in those dense blocks. The overhead introduced by the operations on zeros can become really large and considerably degrade performance. In this paper, we present several techniques for reduc...

This note considers some aspects of the computational problem of by minimizing the sum of absolute deviations Yt = t 1 x· t l3· l= l l fitting the regression model (t = 1, 2, ... , n) r!: 1 x· t l3·1 l= l l The iterative method recently proposed by Schlossmacher (1973) is shown to have undesirable features under certain conditions. The linear programming approach using the simplex method as sug...

This note considers some aspects of the computational problem of k fitting the regression model Yt ~ ti~l Xit~i +~t (t ~ 1, 2, ... , n) by minimizing the sum of absolute deviations ~~lIYt ~=l Xit~il The iterative method recently proposed by Schlossmacher (1973) is shown to have undesirable features under certain conditions. The linear programming approach using the simplex method as suggested b...

Systems of consistent linear equations with symmetric positive semidefinite matrices arise naturally while solving many scientific and engineering problems. In case of a “floating” static structure, the boundary conditions are not sufficient to prevent its rigid body motions. Traditional solvers based on Cholesky decomposition can be adapted to these systems by recognition of zero rows or colum...

We consider the problem of partitioning a matrix of m rows and n columns of non-negative integers into M smaller submatrices. With each submatrix is associated a cost equal to the sum of its elements. The objective is to minimize the cost of the submatrix of maximum cost. We present a (0–1)-integer programming formulation of the problem and three di2erent lower bounds. A heuristic procedure for...