In this paper, a numerical method for nding minimal solution of a mn fullyfuzzy linear system of the form Ax = b based on pseudo inverse calculation,is given when the central matrix of coecients is row full rank or column fullrank, and where A~ is a non-negative fuzzy mn matrix, the unknown vectorx is a vector consisting of n non-negative fuzzy numbers and the constant b isa vector consisting o...

In this note I give a proof of the existence of a Smith normal form for matrices with integer entries. The existence of a good basis for a lattice with a finite index sublattice is a consequence of the Smith normal form. I conclude with an easy application to toric varieties. Theorem 1. Let A be a matrix with integer entries. Then there exist integer-values invertible matrices C and B such that...

where Mk,n is the set of all k-by-n matrices with coefficients in {0, 1} and the variables y l are interpreted as follows: y i l = 1 if and only if z i = l. The matrix (y j) can be seen as a {0, 1} assignment matrix where each column contains exactly one coefficient equal to 1 while h denotes the index of the lowest row that is not identically equal to the zero row (cf. Fig. 1). Another variant...

A new necessary and sufficient condition for the row W-property is given. By using this new condition and a special row rearrangement, we provide two global error bounds for the extended vertical linear complementarity problem under the row W-property, which extend the error bounds given in [2, 10] for the P-matrix linear complementarity problem, respectively. We show that one of the new error ...

In this project, we had to implement a parallel solver for linear equation systems, using a technique known as Gaussian elimination (GE). As with many other algorithms for solving linear equation systems, GE is performed on the matrix representation of the system, Ax = b, where A is the coefficient matrix and b is the vector of known values. GE works by applying a set of elementary row operatio...

* Receive the edge-weight matrix */ if (rcv(MATRIX_TYPE) < 0) { pvm_perror("rcv"); exit(1); } if (getndfloat(matrix, SQR(nodes))) { pvm_perror("getndfloat"); exit(1); } /* Compute the appropriate row of the new matrix */ comp_short_paths(matrix, nodes, inum, newrow); /* Send the new row back to the master */ initsend(); if (putndfloat(newrow, nodes)) { pvm_perror("putndfloat"); exit(1); } if (s...

* Receive the edge-weight matrix */ if (rcv(MATRIX_TYPE) < 0) { pvm_perror("rcv"); exit(1); } if (getndfloat(matrix, SQR(nodes))) { pvm_perror("getndfloat"); exit(1); } /* Compute the appropriate row of the new matrix */ comp_short_paths(matrix, nodes, inum, newrow); /* Send the new row back to the master */ initsend(); if (putndfloat(newrow, nodes)) { pvm_perror("putndfloat"); exit(1); } if (s...