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...

1 The fundamental problem can be extended from p sets each consisting of a pair of variables only one of which can bc nonbasic to k sets of several variables each, only one of which can be nonbasic. To be specific, consider a system w = q f Nz, zw > 0, z > 0, where N is a p x k matrix (k < p) and the variables wl, , zu@ are partitioned into k nonempty sets SI, I = I, ., k. Let TI = SJ IJ {q}, I...

The increasing interest in product networks (PNs) as a method of combining desirable properties of component networks, has prompted a need for the general study of the algorithmic issues related to this important class of interconnection networks. In this paper we present unified parallel algorithms for Gaussian elimination, with partial and complete pivoting, on product networks. A parallel al...

We present a new method for the a priori approximation of the order of magnitude of the entries in the LU factors of a matrix A ∈ Cn×n. We are also able to predict which permutation matrices will be chosen by partial pivoting or complete pivoting Gaussian elimination. Our method uses maxplus algebra and is based purely on the modulii of the entries in the matrix. This approximation can be used ...

Several biomechanical studies have demonstrated the importance of the anterolateral ligament (ALL) in rotational instability of the knee. Despite this, the precise role of the ALL in eliminating the pivot shift remains controversial. This disparity exists secondary to the nature of cadaveric research and the subsequent creation of artificial injury patterns that are not a true representation of...

This paper presents new simple approaches for evaluating determinant and inverse of a matrix. The choice of pivot selection has been kept arbitrary thus they reduce the error while solving an ill conditioned system. Computation of determinant of a matrix has been made more efficient by saving unnecessary data storage and also by reducing the order of the matrix at each iteration, while dictiona...