We survey some unusual eigenvalue problems arising in different applications. We show that all these problems can be cast as problems of estimating quadratic forms. Numerical algorithms based on the well-known Gauss-type quadrature rules and Lanczos process are reviewed for computing these quadratic forms. These algorithms reference the matrix in question only through a matrix-vector product op...

We analyze some models of nonequilibrium systems proposed in the past decade which derive the laws of Irreversible Thermodynamics from deterministic dynamics. We find that these models do not posses the crucial property of local thermodynamic equilibrium, since they represent noninteracting particles systems. Hence, these models are not suited for a derivation of Irreversible Thermodynamics. In...

This paper constructs strong-stability-preserving general linear time-stepping methods that are well suited for hyperbolic PDEs discretized by the method of lines. These methods generalize both Runge–Kutta (RK) and linear multistep schemes. They have high stage orders and hence are less susceptible than RK methods to order reduction from source terms or nonhomogeneous boundary conditions. A glo...

We present a method for the direct generation of the lists of Ž . strings, suited for integral-driven full-CI FCI algorithms. This method generates the string lists each time they are used, and hence sensibly reduces the memory requirements, compared to our previous method that precalculates the lists. It was also extended to permit a truncation of the string space, according to the level of ex...

This paper constructs strong-stability-preserving general linear time-stepping methods that are well suited for hyperbolic PDEs discretized by the method of lines. These methods generalize both Runge-Kutta (RK) and linear multistep schemes. They have high stage orders and hence are less susceptible than RK methods to order reduction from source terms or nonhomogeneous boundary conditions. A glo...

Multilayered feedforward neural networks possess a number of properties which make them particularly suited to complex pattern classification problems. However, their application to some realworld problems has been hampered by the lack of a training algonthm which reliably finds a nearly globally optimal set of weights in a relatively short time. Genetic algorithms are a class of optimization p...

Recent work has suggested that low-density generator matrix (LDGM) codes are likely to be effective for lossy source coding problems. We derive rigorous upper bounds on the effective rate-distortion function of LDGM codes for the binary symmetric source, showing that they quickly approach the rate-distortion function as the degree increases. We also compare and contrast the standard LDGM constr...