28-Jul-2021 14:46:35 line_fekete_rule_test(): MATLAB/Octave version 9.9.0.1467703 (R2020b) Test line_fekete_rule(). line_fekete_rule_bos_levenberg_test: Seek Fekete points in [-1,1] using 1000 equally spaced sample points for polynomial space of dimension M = 5 with the Chebyshev basis and weight 1/sqrt(1-x^2). Estimated Fekete points XF: 1: -1 2: -0.663664 3: -0.00700701 4: 0.641642 5: 1 Saved plot in file "line_fekete_bos_levenberg.png" line_fekete_chebyshev_test: Seek Fekete points in [-1,1] using 1000 equally spaced sample points for polynomials of degree M = 5 with the Chebyshev basis and weight 1/sqrt(1-x^2). NF = 5 Estimated Fekete points XF: 1: -1 2: -0.663664 3: -0.00700701 4: 0.641642 5: 1 Graphics saved as "line_fekete_chebyshev.png" Sum(WF) = 3.14159 line_fekete_legendre_test: Seek Fekete points in [-1,1] using 5001 equally spaced sample points for polynomials of degree M = 5 with the Legendre basis and uniform weight. ind = 1 989 2516 4055 5001 NF = 5 Estimated Fekete points XF: 1: -1 2: -0.6048 3: 0.006 4: 0.6216 5: 1 Graphics saved as "line_fekete_legendre.png" Sum(WF) = 2 line_fekete_monomial_test: Seek Fekete points in [-1,1] using 5001 equally spaced sample points for polynomials of degree M = 5 using the monomial basis and uniform weight. NF = 5 Estimated Fekete points XF: 1: -1 2: -0.656 3: 0 4: 0.6248 5: 1 Graphics saved as "line_fekete_monomial.png" Sum(WF) = 2 line_fekete_rule_bos_levenberg_test: Seek Fekete points in [-1,1] using 1000 equally spaced sample points for polynomial space of dimension M = 11 with the Chebyshev basis and weight 1/sqrt(1-x^2). Estimated Fekete points XF: 1: -1 2: -0.937938 3: -0.791792 4: -0.573574 5: -0.299299 6: -0.003003 7: 0.299299 8: 0.56957 9: 0.78979 10: 0.937938 11: 1 Saved plot in file "line_fekete_bos_levenberg.png" line_fekete_chebyshev_test: Seek Fekete points in [-1,1] using 1000 equally spaced sample points for polynomials of degree M = 11 with the Chebyshev basis and weight 1/sqrt(1-x^2). NF = 11 Estimated Fekete points XF: 1: -1 2: -0.937938 3: -0.791792 4: -0.573574 5: -0.299299 6: -0.003003 7: 0.299299 8: 0.56957 9: 0.78979 10: 0.937938 11: 1 Graphics saved as "line_fekete_chebyshev.png" Sum(WF) = 3.14159 line_fekete_legendre_test: Seek Fekete points in [-1,1] using 5001 equally spaced sample points for polynomials of degree M = 11 with the Legendre basis and uniform weight. ind = 1 195 654 1135 1764 2487 3200 3854 4346 4805 5001 NF = 11 Estimated Fekete points XF: 1: -1 2: -0.9224 3: -0.7388 4: -0.5464 5: -0.2948 6: -0.0056 7: 0.2796 8: 0.5412 9: 0.738 10: 0.9216 11: 1 Graphics saved as "line_fekete_legendre.png" Sum(WF) = 2 line_fekete_monomial_test: Seek Fekete points in [-1,1] using 5001 equally spaced sample points for polynomials of degree M = 11 using the monomial basis and uniform weight. NF = 11 Estimated Fekete points XF: 1: -1 2: -0.8996 3: -0.7056 4: -0.5676 5: -0.4124 6: -0.046 7: 0.3084 8: 0.4948 9: 0.6512 10: 0.8868 11: 1 Graphics saved as "line_fekete_monomial.png" Sum(WF) = 2 line_fekete_rule_bos_levenberg_test: Seek Fekete points in [-1,1] using 1000 equally spaced sample points for polynomial space of dimension M = 21 with the Chebyshev basis and weight 1/sqrt(1-x^2). Estimated Fekete points XF: 1: -1 2: -0.983984 3: -0.943944 4: -0.881882 5: -0.7998 6: -0.6997 7: -0.581582 8: -0.449449 9: -0.307307 10: -0.157157 11: -0.001001 12: 0.153153 13: 0.305305 14: 0.449449 15: 0.581582 16: 0.6997 17: 0.801802 18: 0.883884 19: 0.943944 20: 0.983984 21: 1 Saved plot in file "line_fekete_bos_levenberg.png" line_fekete_chebyshev_test: Seek Fekete points in [-1,1] using 1000 equally spaced sample points for polynomials of degree M = 21 with the Chebyshev basis and weight 1/sqrt(1-x^2). NF = 21 Estimated Fekete points XF: 1: -1 2: -0.983984 3: -0.943944 4: -0.881882 5: -0.7998 6: -0.6997 7: -0.581582 8: -0.449449 9: -0.307307 10: -0.157157 11: -0.001001 12: 0.153153 13: 0.305305 14: 0.449449 15: 0.581582 16: 0.6997 17: 0.801802 18: 0.883884 19: 0.943944 20: 0.983984 21: 1 Graphics saved as "line_fekete_chebyshev.png" Sum(WF) = 3.14159 line_fekete_legendre_test: Seek Fekete points in [-1,1] using 5001 equally spaced sample points for polynomials of degree M = 21 with the Legendre basis and uniform weight. ind = 1 55 186 323 514 747 969 1486 1785 2131 2498 2866 3228 3553 3857 4079 4487 4678 4816 4947 5001 NF = 21 Estimated Fekete points XF: 1: -1 2: -0.9784 3: -0.926 4: -0.8712 5: -0.7948 6: -0.7016 7: -0.6128 8: -0.406 9: -0.2864 10: -0.148 11: -0.0012 12: 0.146 13: 0.2908 14: 0.4208 15: 0.5424 16: 0.6312 17: 0.7944 18: 0.8708 19: 0.926 20: 0.9784 21: 1 Graphics saved as "line_fekete_legendre.png" Sum(WF) = 2 line_fekete_monomial_test: Seek Fekete points in [-1,1] using 5001 equally spaced sample points for polynomials of degree M = 21 using the monomial basis and uniform weight. NF = 21 Estimated Fekete points XF: 1: -1 2: -0.9816 3: -0.95 4: -0.8932 5: -0.8324 6: -0.7228 7: -0.5588 8: -0.4528 9: -0.3268 10: -0.1552 11: 0.0132 12: 0.1692 13: 0.3184 14: 0.4524 15: 0.5972 16: 0.7368 17: 0.838 18: 0.8968 19: 0.9516 20: 0.9824 21: 1 Graphics saved as "line_fekete_monomial.png" Sum(WF) = 2 line_fekete_rule_bos_levenberg_test: Seek Fekete points in [-1,1] using 1000 equally spaced sample points for polynomial space of dimension M = 41 with the Chebyshev basis and weight 1/sqrt(1-x^2). Estimated Fekete points XF: 1: -1 2: -0.995996 3: -0.985986 4: -0.96997 5: -0.947948 6: -0.91992 7: -0.887888 8: -0.84985 9: -0.805806 10: -0.757758 11: -0.703704 12: -0.647648 13: -0.585586 14: -0.521522 15: -0.453453 16: -0.383383 17: -0.309309 18: -0.235235 19: -0.157157 20: -0.0810811 21: -0.001001 22: 0.0770771 23: 0.157157 24: 0.233233 25: 0.309309 26: 0.381381 27: 0.453453 28: 0.521522 29: 0.585586 30: 0.647648 31: 0.703704 32: 0.757758 33: 0.805806 34: 0.84985 35: 0.887888 36: 0.91992 37: 0.947948 38: 0.96997 39: 0.985986 40: 0.995996 41: 1 Saved plot in file "line_fekete_bos_levenberg.png" line_fekete_chebyshev_test: Seek Fekete points in [-1,1] using 1000 equally spaced sample points for polynomials of degree M = 41 with the Chebyshev basis and weight 1/sqrt(1-x^2). NF = 41 Estimated Fekete points XF: 1: -1 2: -0.995996 3: -0.985986 4: -0.96997 5: -0.947948 6: -0.91992 7: -0.887888 8: -0.84985 9: -0.805806 10: -0.757758 11: -0.703704 12: -0.647648 13: -0.585586 14: -0.521522 15: -0.453453 16: -0.383383 17: -0.309309 18: -0.235235 19: -0.157157 20: -0.0810811 21: -0.001001 22: 0.0770771 23: 0.157157 24: 0.233233 25: 0.309309 26: 0.381381 27: 0.453453 28: 0.521522 29: 0.585586 30: 0.647648 31: 0.703704 32: 0.757758 33: 0.805806 34: 0.84985 35: 0.887888 36: 0.91992 37: 0.947948 38: 0.96997 39: 0.985986 40: 0.995996 41: 1 Graphics saved as "line_fekete_chebyshev.png" Sum(WF) = 3.14159 line_fekete_legendre_test: Seek Fekete points in [-1,1] using 5001 equally spaced sample points for polynomials of degree M = 41 with the Legendre basis and uniform weight. ind = 1 15 50 86 136 244 311 406 506 622 750 885 1042 1206 1362 1512 1699 1845 2171 2331 2524 2697 2880 3060 3232 3410 3559 3845 3967 4108 4250 4382 4497 4596 4690 4758 4866 4916 4952 4987 5001 NF = 41 Estimated Fekete points XF: 1: -1 2: -0.9944 3: -0.9804 4: -0.966 5: -0.946 6: -0.9028 7: -0.876 8: -0.838 9: -0.798 10: -0.7516 11: -0.7004 12: -0.6464 13: -0.5836 14: -0.518 15: -0.4556 16: -0.3956 17: -0.3208 18: -0.2624 19: -0.132 20: -0.068 21: 0.0092 22: 0.0784 23: 0.1516 24: 0.2236 25: 0.2924 26: 0.3636 27: 0.4232 28: 0.5376 29: 0.5864 30: 0.6428 31: 0.6996 32: 0.7524 33: 0.7984 34: 0.838 35: 0.8756 36: 0.9028 37: 0.946 38: 0.966 39: 0.9804 40: 0.9944 41: 1 Graphics saved as "line_fekete_legendre.png" Sum(WF) = 2 line_fekete_monomial_test: Seek Fekete points in [-1,1] using 5001 equally spaced sample points for polynomials of degree M = 41 using the monomial basis and uniform weight. [Warning: Rank deficient, rank = 36, tol = 7.110318e-12.] [> In line_fekete_monomial (line 81) In line_fekete_monomial_test (line 46) In line_fekete_rule_test (line 31) In run (line 91) ] NF = 36 Estimated Fekete points XF: 1: -1 2: -0.9912 3: -0.9756 4: -0.948 5: -0.9184 6: -0.892 7: -0.8596 8: -0.8164 9: -0.7712 10: -0.6964 11: -0.5908 12: -0.5328 13: -0.4716 14: -0.4004 15: -0.3292 16: -0.256 17: -0.1764 18: -0.0284 19: 0.0372 20: 0.1052 21: 0.238 22: 0.3648 23: 0.4256 24: 0.4888 25: 0.5712 26: 0.6532 27: 0.7344 28: 0.776 29: 0.812 30: 0.874 31: 0.9176 32: 0.9488 33: 0.974 34: 0.9908 35: 0.9968 36: 1 Graphics saved as "line_fekete_monomial.png" Sum(WF) = 2 line_fekete_rule_test(): Normal end of execution. 28-Jul-2021 14:46:43