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chebyshev2_exactness_test:
MATLAB/Octave version 9.9.0.1467703 (R2020b).
Test chebyshev2_exactness.
27-Jul-2021 20:35:17
CHEBYSHEV2_EXACTNESS
MATLAB/Octave version 9.9.0.1467703 (R2020b)
Investigate the polynomial exactness of a Gauss-Chebyshev1
type 2 quadrature rule by integrating all monomials up to a given
degree over the [-1,+1] interval.
CHEBYSHEV2_EXACTNESS: User input:
Quadrature rule X file = "cheby2_o4_x.txt".
Quadrature rule W file = "cheby2_o4_w.txt".
Quadrature rule R file = "cheby2_o4_r.txt".
Maximum degree to check = 10
Spatial dimension = 1
Number of points = 4
The quadrature rule to be tested is
a Gauss-Chebyshev type 2 rule
ORDER = 4
Standard rule:
Integral ( -1 <= x <= +1 ) f(x) * ( 1 - x^2 ) dx
is to be approximated by
sum ( 1 <= I <= ORDER ) w(i) * f(x(i)).
Weights W:
w(1) = 0.2170787134227061
w(2) = 0.5683194499747424
w(3) = 0.5683194499747423
w(4) = 0.2170787134227060
Abscissas X:
x(1) = -0.8090169943749473
x(2) = -0.3090169943749473
x(3) = 0.3090169943749475
x(4) = 0.8090169943749475
Region R:
r(1) = -1.000000e+00
r(2) = 1.000000e+00
A Gauss-Chebyshev type 2 rule would be able to exactly
integrate monomials up to and including
degree = 7
Error Degree
0.0000000000000001 0
0.0000000000000000 1
0.0000000000000000 2
0.0000000000000000 3
0.0000000000000001 4
0.0000000000000000 5
0.0000000000000001 6
0.0000000000000000 7
0.0714285714285715 8
0.0000000000000000 9
0.1904761904761904 10
CHEBYSHEV2_EXACTNESS:
Normal end of execution.
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chebyshev2_exactness_test:
Normal end of execution.
27-Jul-2021 20:35:17