**Commenced**in January 2007

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**Edition:**International

**Paper Count:**30172

##### Quadrature Formula for Sampled Functions

**Authors:**
Khalid Minaoui,
Thierry Chonavel,
Benayad Nsiri,
Driss Aboutajdine

**Abstract:**

This paper deals with efficient quadrature formulas involving functions that are observed only at fixed sampling points. The approach that we develop is derived from efficient continuous quadrature formulas, such as Gauss-Legendre or Clenshaw-Curtis quadrature. We select nodes at sampling positions that are as close as possible to those of the associated classical quadrature and we update quadrature weights accordingly. We supply the theoretical quadrature error formula for this new approach. We show on examples the potential gain of this approach.

**Keywords:**
Gauss-Legendre,
Clenshaw-Curtis,
quadrature,
Peano kernel,
irregular sampling.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1327488

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