In this paper we propose a local spline method for the approximation of the derivative of a function f . It is based on an optimal spline quasi-interpolant operator Q_2, introduced in . Differentiating Q_2 f , we construct the pseudo-spectral derivative at the quasi-interpolation knots and the corresponding differentiation matrix. An error analysis is proposed. Some numerical results and comparisons with other known methods are given.

### Pseudo-spectral derivative of quadratic quasi-interpolant splines

#### Abstract

In this paper we propose a local spline method for the approximation of the derivative of a function f . It is based on an optimal spline quasi-interpolant operator Q_2, introduced in . Differentiating Q_2 f , we construct the pseudo-spectral derivative at the quasi-interpolation knots and the corresponding differentiation matrix. An error analysis is proposed. Some numerical results and comparisons with other known methods are given.
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Quasi-interpolant splines; Pseudo-spectral derivative; Differentiation matrix
S. Remogna
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/2318/99131`
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