We present Neumann-Neumann domain decomposition preconditioners for the solution of elliptic linear quadratic optimal control problems. The preconditioner is applied to the optimality system. A Schur complement formulation is derived that reformulates the original optimality system as a system in the state and adjoint variables restricted to the subdomain boundaries. The application of the Schu...

Symm’s equation is a first-kind integral equation for computing conformal maps of simply connected regions. The package CONFPACK solves Symm’s equation by an indirect boundary element method using an accurate corner representation. This solution technique is extended here to include nonoverlapping domain decomposition. Degrees of freedom are introduced on one or more interfaces and different un...

Structured singular values and pseudospectra play an important role in assessing the properties of a linear system under structured perturbations. This paper discusses computational aspects of structured pseudospectra for structures that admit an eigenvalue minimization characterization, including the classes of real, skew-symmetric, Hermitian, and Hamiltonian perturbations. For all these struc...

In this paper, I show how to use the generalized Schur form to solve a system of linear expectational di!erence equations (a multivariate linear rational expectations model). The method is simple to understand and to use, and is applicable to a large class of rational expectations models. The only hard part is taken care of by just two standard algorithms, both of which are available as freewar...

This talk concerns a preconditioning method of AMLI type [3] for the solution of linear partial differential equations systems. An earlier idea of this study was proposed in [2] for scalar case. In this work we want to make some further extension of the study done in [1], in particular we propose to give a robust preconditioning iterative schemes using domain decomposition methods. Based on a s...

Let F denote the Fock space representation of the quantum groupUv(ŝle). The ‘v-decomposition numbers’ are the coefficients when the canonical basis for this representation is expanded in terms of the basis of partitions, and the evaluations at v = 1 of these polynomials give the decomposition numbers for Iwahori–Hecke algebras and q-Schur algebras over C. James and Mathas have proved a theorem ...

Presented are two related numerical methods, one for the inverse eigenvalue problem for nonnegative or stochastic matrices and another for the inverse eigenvalue problem for symmetric nonnegative matrices. The methods are iterative in nature and utilize alternating projection ideas. For the symmetric problem, the main computational component of each iteration is an eigenvalue-eigenvector decomp...

The spectral decomposition of the path space of the vertex model associated to the level l representation of the quantized affine algebra Uq(ŝln) is studied. The spectrum and its degeneracy are parametrized by skew Young diagrams and what we call nonmovable tableaux on them, respectively. As a result we obtain the characters for the degeneracy of the spectrum in terms of an alternating sum of s...

This paper presents a Domain Decomposition-type method for solving real symmetric (or Hermitian complex) eigenvalue problems in which we seek all eigenpairs in an interval [α, β], or a few eigenpairs next to a given real shift ζ. A Newton-based scheme is described whereby the problem is converted to one that deals with the interface nodes of the computational domain. This approach relies on the...

Vandermonde, Cauchy, and Cauchy–Vandermonde totally positive linear systems can be solved extremely accurately in O(n2) time using Björck–Pereyra-type methods. We prove that Björck–Pereyra-type methods exist not only for the above linear systems but also for any totally positive linear system as long as the initial minors (i.e., contiguous minors that include the first row or column) can be com...