Iterative methods for discrete nonlinear Riemann-Hilbert problems

Generalized orthogonal polynomials, discrete KP and Riemann-Hilbert problems

Classically, a single weight on an interval of the real line leads to moments, orthogonal polynomials and tridiagonal matrices. Appropriately deforming this weight with times t = (t1, t2, ...), leads to the standard Toda lattice and τ -functions, expressed as Hermitian matrix integrals. This paper is concerned with a sequence of t-perturbed weights, rather than one single weight. This sequence ...

Nonlinear Riemann-hilbert Problem for Bordered Riemann Surfaces

Let Σ be a bordered Riemann surface with genus g and m boundary components. Let {γz}z∈∂Σ be a smooth family of smooth Jordan curves in C which all contain the point 0 in their interior. Then there exists a holomorphic function f(z) on Σ smooth up to the boundary with at most 2g +m− 1 zeros on Σ such that f(z) ∈ γz for every z ∈ ∂Σ.

Riemann-Hilbert problems for last passage percolation

Last three years have seen new developments in the theory of last passage percolation, which has variety applications to random permutations, random growth and random vicious walks. It turns out that a few class of models have determinant formulas for the probability distribution, which can be analyzed asymptotically. One of the tools for the asymptotic analysis has been the Riemann-Hilbert met...

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

Iterative Solution Methods for Large Linear Discrete Ill-posed Problems

This paper discusses iterative methods for the solution of very large severely ill-conditioned linear systems of equations that arise from the discretization of linear ill-posed problems. The right-hand side vector represents the given data and is assumed to be contaminated by errors. Solution methods proposed in the literature employ some form of ltering to reduce the in uence of the error in ...