The eeciency of solving sparse linear systems on parallel processors and more complex multicluster architectures such as Cedar is greatly enhanced if relatively large grain computational tasks can be assigned to each cluster or processor. The ordering of a system into a bordered block upper triangular form facilitates a reasonable large-grain partitioning. A new algorithm which produces this fo...

In this paper, we analyze matrix dynamics for online linear discriminant analysis (online LDA). Convergence of the dynamics have been studied for nonsingular cases; our main contribution is an analysis of singular cases, that is a key for efficient calculation without full-size square matrices. All fixed points of the dynamics are identified and their stability is examined. © 2010 Elsevier Inc....

Álvarez et al. (Information Sciences, Vol. 179, Issue 12, 2009) proposed a new key exchange scheme where the secret key is obtained by multiplying powers of block upper triangular matrices whose elements are defined over Zp. In this note, we show that breaking this system with security parameters (r, s, p) is equivalent to solving a set of 3(r + s) linear equations with 2(r+s) unknowns in Zp, w...

It is well-known by now that `1 minimization can help recover sparse solutions to under-determined linear equations or sparsely corrupted solutions to over-determined equations, and the two problems are equivalent under appropriate conditions. So far almost all theoretic results have been obtained through studying the “under-determined side” of the problem. In this note, we take a different app...

Motivated by the advantages achieved by implicit analogue net for solving online linear equations, a novel implicit neural model is designed based on conventional explicit gradient neural networks in this letter by introducing a positive-definite mass matrix. In addition to taking the advantages of the implicit neural dynamics, the proposed implicit gradient neural networks can still achieve gl...

A method is presented for solving the momentum-space Schrödinger equation with a linear potential. The Lande-subtracted momentum-space integral equation can be transformed into a matrix equation by the Nystrom method. The method produces only approximate eigenvalues in the cases of singular potentials such as the linear potential. The eigenvalues generated by the Nystrom method can be improved ...

Abstract. We present a new tunably accurate Laguerre Petrov–Galerkin spectral method for solving linear multiterm fractional initial value problems with derivative orders at most one and constant coefficients on the half line. Our method results in a matrix equation of special structure which can be solved in O(N logN) operations. We also take advantage of recurrence relations for the generaliz...

We give a derivation of the loop equation for two-dimensional gravity from the KdV equations and the string equation of the one matrix model. We find that the loop equation is equivalent to an infinite set of linear constraints on the square root of the partition function satisfying the Virasoro algebra. We give an interpretation of these equations in topological gravity and discuss their exten...

the edge detour index polynomials were recently introduced for computing theedge detour indices. in this paper we nd relations among edge detour polynomials for the2-dimensional graph of tuc4c8(s) in a euclidean plane and tuc4c8(s) nanotorus.

We consider the numerical solution of the continuous algebraic Riccati equation AX +XA−XFX +G = 0, with F = F , G = G of low rank and A large and sparse. We develop an algorithm for the low rank approximation of X by means of an invariant subspace iteration on a function of the associated Hamiltonian matrix. We show that the sought after approximation can be obtained by a low rank update, in th...