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 ...

Let A ⊂ L2(R) be at most countable, and p, q ∈ N. We characterize various frame-properties for Gabor systems of the form G(1, p/q,A)= {e2 g(x − np/q) : m, n ∈ Z, g ∈ A} in terms of the corresponding frame properties for the row vectors in the Zibulski–Zeevi matrix. This extends work by [Ron and Shen, Weyl–Heisenberg systems and Riesz bases in L2(R d). Duke Math. J. 89 (1997) 237–282], who consi...

A circulant matrix of order n is the matrix of convolution by a fixed element of the group algebra of the cyclic group Zn. Replacing Zn by an arbitrary finite group G gives the class of matrices that we call G-circulant. We determine the eigenvalues of such matrices with the tools of representation theory and the non-abelian Fourier transform. Definition 1 An n by n matrix C is circulant if the...

In the early 1950’s, M. G. Krein characterized the entire functions that are an entry of some Nevanlinna matrix, and the pairs of entire functions that are a row of some Nevanlinna matrix. In connection with Pontryagin space versions of Krein’s theory of entire operators and de Branges’ theory of Hilbert spaces of entire functions, an indefinite analog of the Nevanlinna matrices plays a role. I...

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...

We consider the related tasks of matrix completion and matrix approximation from missing data and propose adaptive sampling procedures for both problems. We show that adaptive sampling allows one to eliminate standard incoherence assumptions on the matrix row space that are necessary for passive sampling procedures. For exact recovery of a low-rank matrix, our algorithm judiciously selects a fe...