An extension to rational functions of a theorem of J. L. Walsh on differences of interpolating polynomials
The main result says in particular that if is a trigonometric polynomial of degree n having all its zeros in the open upper half-plane such that |t(ξ)| ≥ μ on the real axis and cₙ ≠ 0, then |t’(ξ)| ≥ μn for all real ξ.
This paper is an introduction to formal orthogonal polynomials and their application to Padé approximation, Krylov subspace methods for the solution of systems of linear equations, and convergence acceleration methods. Some more general formal orthogonal polynomials, and the concept of biorthogonality and its applications are also discussed.
Mediante integrali multipli agevoli per il calcolo numerico vengono espressi il valore assoluto di un determinante qualsiasi e le formule di Cramer.