We give a theoretical explanation for superlinear convergence behavior observed while solving large symmetric systems of equations using the conjugate gradient method or other Krylov subspaceâ€¦ (More)

We show that the average characteristic polynomial Pn(z) = E[det(zIâˆ’M)] of the random Hermitian matrix ensemble Z n exp(âˆ’Tr(V (M) âˆ’ AM))dM is characterized by multiple orthogonality conditions thatâ€¦ (More)

We continue the study of the Hermitian random matrix ensemble with external source 1 Zn e âˆ’nTr( 1 2 M 2 âˆ’AM) dM where A has two distinct eigenvalues Â±a of equal multiplicity. This model exhibits aâ€¦ (More)

We consider polynomials that are orthogonal on [âˆ’1, 1] with respect to a modified Jacobi weight (1 âˆ’ x)Î±(1 + x)Î²h(x), with Î±, Î² > âˆ’1 and h real analytic and stricly positive on [âˆ’1, 1]. We obtainâ€¦ (More)

We present a generalization of multiple orthogonal polynomials of type I and type II, which we call multiple orthogonal polynomials of mixed type. Some basic properties are formulated, and aâ€¦ (More)

The equilibrium measure in the presence of an external eld plays a role in a number of areas in analysis, for example in random matrix theory: the limiting mean density of eigenvalues is preciselyâ€¦ (More)

It is shown that no stable procedure for approximating functions from equally spaced samples can converge exponentially for analytic functions. To avoid instability, one must settle forâ€¦ (More)

We study the zeros of orthogonal polynomials pn,N , n = 0, 1, . . ., that are generated by recurrence coefficients an,N and bn,N depending on a parameter N . Assuming that the recurrence coefficientsâ€¦ (More)

We study unitary random matrix ensembles of the form Zâˆ’1 n,N | detM | 2Î±eâˆ’N TrV dM, where Î± > âˆ’1/2 and V is such that the limiting mean eigenvalue density for n,N â†’ âˆž and n/N â†’ 1 vanishesâ€¦ (More)