We investigate the uniform convergence of Lagrange interpolation at the zeros of the orthogonal polynomials with respect to a Freud-type weight in the presence of constraints. We show that by a simple procedure it is always possible to transform the matrices of these zeros into matrices such that the corresponding Lagrange interpolating polynomial with re- spect to the given constraints well approximates a given function. This procedure was, at ¯rst, successfully introduced for the polynomial inter- polation with constraints on bounded intervals [1]. For this procedure we obtain the same results obtained in [10], where only the zeros of the orthogonal polynomials are used.
Lagrange interpolation with constraints on the real line / M. R., Capobianco; Criscuolo, Giuliana. - 17:(2013), pp. 51-60.
Lagrange interpolation with constraints on the real line
CRISCUOLO, GIULIANA
2013
Abstract
We investigate the uniform convergence of Lagrange interpolation at the zeros of the orthogonal polynomials with respect to a Freud-type weight in the presence of constraints. We show that by a simple procedure it is always possible to transform the matrices of these zeros into matrices such that the corresponding Lagrange interpolating polynomial with re- spect to the given constraints well approximates a given function. This procedure was, at ¯rst, successfully introduced for the polynomial inter- polation with constraints on bounded intervals [1]. For this procedure we obtain the same results obtained in [10], where only the zeros of the orthogonal polynomials are used.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.