# square_minimal_rule

square_minimal_rule, a C++ code which returns "almost minimal" quadrature rules, with exactness up to total degree 55, over the interior of the symmetric unit square in 2D, by Mattia Festa and Alvise Sommariva.

### Languages:

square_minimal_rule is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

### Related Data and Programs:

ANNULUS_RULE, a C++ code which computes a quadrature rule for estimating integrals of a function over the interior of a circular annulus in 2D.

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SQUARE_SYMQ_RULE, a C++ code which returns efficient symmetric quadrature rules, with exactness up to total degree 15, over the interior of a symmetric square in 2D, by Hong Xiao and Zydrunas Gimbutas.

STROUD, a C++ code which defines quadrature rules for a variety of M-dimensional regions, including the interior of the square, cube and hypercube, the pyramid, cone and ellipse, the hexagon, the M-dimensional octahedron, the circle, sphere and hypersphere, the triangle, tetrahedron and simplex, and the surface of the circle, sphere and hypersphere.

TOMS886, a C++ code which defines the Padua points for interpolation in a 2D region, including the rectangle, triangle, and ellipse, by Marco Caliari, Stefano de Marchi, Marco Vianello. This is a version of ACM TOMS algorithm 886.

### Reference:

1. Mattia Festa, Alvise Sommariva,
Computing almost minimal formulas on the square,
Journal of Computational and Applied Mathematics,
Volume 17, Number 236, November 2012, pages 4296-4302.

### Source Code:

Last revised on 19 April 2020.