hexagon_lyness_rule

hexagon_lyness_rule, an Octave code which returns one of 13 Lyness quadrature rules over the interior of the unit hexagon.

The Lyness rules assume the hexagon has a "peaked top and bottom:

             *
          *     *
          *     *
             * 
    

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

hexagon_lyness_rule is available in a MATLAB version and an Octave version..

Related Data and Programs:

hexagon_lyness_rule_test

octave_rule, an Octave code which computes a quadrature rule which estimates the integral of a function f(x), which might be defined over a one dimensional region (a line) or more complex shapes such as a circle, a triangle, a quadrilateral, a polygon, or a higher dimensional region, and which might include an associated weight function w(x).

Reference:

1. James Lyness, Giovanni Monegato,
   Quadrature rules for regions having regular hexagonal symmetry,
   SIAM Journal on Numerical Analysis.
   Volume 14 Number 2, April 1977, pages 283-295.

Source Code:

• hexagon01_area.m, returns the area of the unit hexagon.
• hexagon_lyness_rule01.m, Lyness rule 01.
• hexagon_lyness_rule02.m, Lyness rule 02.
• hexagon_lyness_rule03.m, Lyness rule 03.
• hexagon_lyness_rule04.m, Lyness rule 04.
• hexagon_lyness_rule05.m, Lyness rule 05.
• hexagon_lyness_rule06.m, Lyness rule 06.
• hexagon_lyness_rule07.m, Lyness rule 07.
• hexagon_lyness_rule08.m, Lyness rule 08.
• hexagon_lyness_rule09.m, Lyness rule 09.
• hexagon_lyness_rule10.m, Lyness rule 10.
• hexagon_lyness_rule11.m, Lyness rule 11.
• hexagon_lyness_rule12.m, Lyness rule 12.
• hexagon_lyness_rule13.m, Lyness rule 13.
• monomial_value_2d.m, returns the value of a monomial x^ex y^ey.