This paper deals with the average-case-analysis of the number of pivot steps required by the simplex method. It generalizes results of Borgwardt (who worked under the assumpution of the rotation-symmetry-model) for the shadow-vertex-algorithm to so-called cylindric distributions. Simultaneously it allows to analyze an extended dimension-by-dimension-algorithm, which solves linear programing pro...

Many statistical applications require the solution of a symmetric positive definite covariance matrix, sometimes with a large number of right-hand sides of a statistical independence nature. With preconditioning, the preconditioned matrix has almost all the eigenvalues clustered within a narrow range, except for a few extreme eigenvalues deviating from the range rapidly. We derive a deflated ve...

In this survey we address three of the principal algebraic approaches to integer programming. After introducing lattices and basis reduction, we 0rst survey their use in integer programming, presenting among others Lenstra’s algorithm that is polynomial in 0xed dimension, and the solution of diophanine equations using basis reduction. The second topic concerns augmentation algorithms and test s...

Iteration theories, as introduced by Stephen Bloom and Zoltán Ésik, are Lawvere theories equipped with a function assigning to every morphism e : n → n + k (representing a system of n recursive equations whose left-hand sides are variables and right-hand sides are terms in those n variables and k parameters) a morphism e† : n → k (representing a solution of those equations). This function is re...

Uniqueness of normal forms (UN=) is an important property of term rewrite systems. UN= is decidable for ground (i.e., variable-free) systems and undecidable in general. Recently it was shown to be decidable for linear, shallow systems. We generalize this previous result and show that this property is decidable for shallow rewrite systems, in contrast to confluence, reachability and other proper...

We prove that the subset sum problem ax = β x ∈ {0, 1}n (SUB) has a polynomial time computable certificate of infeasibility for all a with density at most 1/(2n), and for almost all β integer right hand sides. The certificate is branching on a hyperplane, i.e. by a methodology dual to the one explored by Lagarias and Odlyzko [6]; Frieze [3]; Furst and Kannan [4]; and Coster et. al. in [1]. We p...

In this paper, we investigate the block Lanczos algorithm for solving large sparse symmetric linear systems with multiple right-hand sides, and show how to incorporate deeation to drop converged linear systems using a natural convergence criterion, and present an adaptive block Lanczos algorithm. We propose also a block version of Paige and Saun-ders' MINRES method for iterative solution of sym...

We present a new algorithm which computes a partial approximate solution for a system of equations. It is local in that it considers as few variables as necessary in order to compute the values of those variables we are interested in, it is generic in that it makes no assumptions on the application domain, and it is general in that the algorithm does not depend on any speciic properties of righ...

With the development of the VLSI circuits, the feature size has been decreased to the deep sub-micron level, and the working frequency has reached to 3GHz. In order to assure the correctness of the IC design with high performance, the parasitic interconnect inductance and resistance should he calculated quickly and accurately. In this paper, the multipole method with modified non-uniform cube p...