SPARSE_GRID_TOTAL_POLY
Total Polynomial Approximation with Sparse Grids

SPARSE_GRID_TOTAL_POLY is a MATLAB library which investigates the limits of total polynomial approximation using sparse grids.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Related Data and Programs:

NINT_EXACTNESS, a MATLAB program which measures the polynomial exactness of an M-dimensional quadrature rule defined over a finite rectangular product region.

SPARSE_GRID_CC, a MATLAB library which creates sparse grids based on Clenshaw-Curtis rules.

Reference:

1. Philip Davis, Philip Rabinowitz,
   Methods of Numerical Integration,
   Second Edition,
   Dover, 2007,
   ISBN: 0486453391,
   LC: QA299.3.D28.

Source Code:

• ccc_nested_rule.m computes the nested Clenshaw Curtis Closed rule.
• ccc_rule.m computes a Clenshaw Curtis closed rule.
• cco_nested_rule.m computes the nested Clenshaw Curtis Open rule.
• cco_rule.m computes a Clenshaw Curtis open rule.
• ccoh_nested_rule.m computes the nested Clenshaw Curtis Open Half rule.
• ccoh_rule.m computes a Clenshaw Curtis Open Half rule.
• i4_log_2.m returns the integer part of the logarithm base 2 of |I|.
• lagrange_factor.m evaluates the polynomial Lagrange factor at a point.
• nc_compute.m computes a Newton-Cotes quadrature rule.
• ncc_nested_rule.m computes the nested Newton Cotes Closed rule.
• ncc_rule.m computes the Newton Cotes Closed rule.
• nco_nested_rule.m computes the nested Newton Cotes Open rule.
• nco_rule.m computes the Newton Cotes Open rule.
• ncoh_nested_rule.m computes the nested Newton Cotes Open Half rule.
• ncoh_rule.m Newton Cotes Open Half quadrature rule.
• ccc_rule.m
• timestamp.m prints the current YMDHMS date as a timestamp.
• vdc_numerator_sequence.m van der Corput numerator sequence base 2.
• vdc_sequence.m N elements of a van der Corput sequence base 2

Examples and Tests:

• sparse_grid_total_poly_test.m tests the SPARSE_GRID_TOTAL_POLY library by calling all the tests.
• sparse_grid_total_poly_test_output.txt the output file.
• point_quality_test.m computes the point quality for quadrature rules.
• rule_test.m tests a rule simply by printing out some examples of it.
• rules_test.m calls RULE_TEST for each of the rules.
• weight_quality_test.m computes the weight quality for quadrature rules.

You can go up one level to the MATLAB source codes.