It is shown that monic orthogonal polynomials on the unit circle are the characteristic polynomials of certain five-diagonal matrices depending on the Schur parameters. This result is achieved through the study of orthogonal Laurent polynomials on the unit circle. More precisely, it is a consequence of the five term recurrence relation obtained for these orthogonal Laurent polynomials, and the ...

Results on multiple orthogonal polynomials will be surveyed. Multiple orthogonal polynomials are intimately related to Hermite–Pad e approximants and often they are also called Hermite–Pad e polynomials. Special attention will be paid to an application of multiple orthogonal polynomials and to analytic theory of two model families of general multiple orthogonal polynomials, referred to as Angel...

In this paper a brief survey of multiple orthogonal polynomials defined using orthogonality conditions spread out over r different measures are given. We consider multiple orthogonal polynomials on the real line, as well as on the unit semicircle in the complex plane. Such polynomials satisfy a linear recurrence relation of order r+1, which is a generalization of the well known three-term recur...