1,721,026 research outputs found
Extended Lagrange interpolation in weighted uniform norm
No full textThe author studies the uniform convergence of extended Lagrange interpolation processes based on the zeros of Generalized Laguerre polynomials.
Introduciont: Let .. and ... be two weight functions, both of them supported in ...
A METHOD TO EVALUATE THE HILBERT TRANSFORM ON (0,∞)
No full textThe author proposes a method to approximate the Hilbert transform on the real positive semiaxis by a suitable Lagrange interpolating polynomial. The method employs truncated Gaussian rules and uses the interlacing properties of the zeros of generalized Laguerre polynomials. The error estimate in a weighted uniform norm is proved and some numerical tests show the efficacy of the proposed procedure
Una buona matrice di nodi
No full textAn interpolation process on the zeros of a product of three orthogonal polynomials and on additional knots is studied
Lagrange interpolation on the semiaxis
Full text linkIn this brief survey are collected some recent results about optimal interpolation processes of Lagrange type based on the zeros of generalized Laguerre polynomials, i.e. the sequence of orthogonal polynomials where A new extended Lagrange process having optimal Lebesgue constants is also introduced
Approximation of a weighted Hilbert transform by using perturbed Laguerre zeros
Full text linkIn the present paper is proposed a numerical method to approximate Hilbert transforms of the type (Formula Presented.), where w(x) = e-xxa, a >-1 is a Laguerre weight, by means of a new Lagrange interpolation process essentially based on the midpoints between two consecutive zeros of Laguerre polynomials. Theoretical error estimates are proved in some weighted uniform spaces and some numerical tests which confirm the theoretical estimates are shown
Convergence of extended Lagrange interpolation in weighted L_p norm
No full textIn this paper we study the convergence in weigthted Lp norm of an extended interpolation process on the zeros of a polynomial product of three orthogonal polynomials and on additional knots
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