25-Mar-2024 22:44:23 cpr_test(): MATLAB/Octave version 9.14.0.2306882 (R2023a) Update 4 Test cpr(), which uses the Chebyshev Proxy Rootfinder to determine all real zeros of a smooth function over an interval [a,b]. bessel_test(): Seek real roots of the J0 Bessel function. all_roots_in_xi = -3.3084 + 0.0000i -0.8894 + 1.3797i -0.8894 - 1.3797i 0.8257 + 1.3902i 0.8257 - 1.3902i -1.0655 + 0.9791i -1.0655 - 0.9791i -1.1658 + 0.7051i -1.1658 - 0.7051i -1.2246 + 0.4965i -1.2246 - 0.4965i -1.2551 + 0.3305i -1.2551 - 0.3305i -1.2642 + 0.1950i -1.2642 - 0.1950i -1.2559 + 0.0833i -1.2559 - 0.0833i -1.2413 + 0.0000i -1.1202 + 0.0000i 1.0092 + 0.9922i 1.0092 - 0.9922i -0.8798 + 0.0000i 1.1165 + 0.7197i 1.1165 - 0.7197i -0.7240 + 0.0000i -0.5673 + 0.0000i 1.1823 + 0.5120i 1.1823 - 0.5120i -0.4104 + 0.0000i -0.2535 + 0.0000i 1.2197 + 0.3466i 1.2197 - 0.3466i 1.2353 + 0.2117i 1.2353 - 0.2117i 1.2334 + 0.0999i 1.2334 - 0.0999i 1.2239 + 0.0000i 1.1605 + 0.0000i 1.0029 + 0.0000i -0.0964 + 0.0000i 0.0606 + 0.0000i 0.8459 + 0.0000i 0.2176 + 0.0000i 0.6888 + 0.0000i 0.3747 + 0.0000i 0.5317 + 0.0000i evi = -3.3084 evi = -0.8894 + 1.3797i evi = -0.8894 - 1.3797i evi = 0.8257 + 1.3902i evi = 0.8257 - 1.3902i evi = -1.0655 + 0.9791i evi = -1.0655 - 0.9791i evi = -1.1658 + 0.7051i evi = -1.1658 - 0.7051i evi = -1.2246 + 0.4965i evi = -1.2246 - 0.4965i evi = -1.2551 + 0.3305i evi = -1.2551 - 0.3305i evi = -1.2642 + 0.1950i evi = -1.2642 - 0.1950i evi = -1.2559 + 0.0833i evi = -1.2559 - 0.0833i evi = -1.2413 evi = -1.1202 evi = 1.0092 + 0.9922i evi = 1.0092 - 0.9922i evi = -0.8798 evi = 1.1165 + 0.7197i evi = 1.1165 - 0.7197i evi = -0.7240 evi = -0.5673 evi = 1.1823 + 0.5120i evi = 1.1823 - 0.5120i evi = -0.4104 evi = -0.2535 evi = 1.2197 + 0.3466i evi = 1.2197 - 0.3466i evi = 1.2353 + 0.2117i evi = 1.2353 - 0.2117i evi = 1.2334 + 0.0999i evi = 1.2334 - 0.0999i evi = 1.2239 evi = 1.1605 evi = 1.0029 evi = -0.0964 evi = 0.0606 evi = 0.8459 evi = 0.2176 evi = 0.6888 evi = 0.3747 evi = 0.5317 Interstitial interpolation error norm = 8.54872e-15 Number of roots = 12 Roots computed by CPR: 2.4048 5.5201 8.6537 11.7915 14.9309 18.0711 21.2116 24.3525 27.4935 30.6346 33.7758 36.9171 Maximum residual at roots = 3.51771e-14 Exact roots: 2.4048 5.5201 8.6537 11.7915 14.9309 18.0711 21.2116 24.3525 27.4935 30.6346 33.7758 36.9171 Exact f(roots): 1.0e-15 * 0 0.0723 0.1065 -0.5891 -0.9230 -0.7815 0.2301 -0.7226 0.7873 0.5897 0.1996 -0.8113 f ( froots ): 1.0e-13 * -0.3518 0.1910 -0.0301 0.0428 -0.0355 -0.1000 -0.0537 0.0732 0.0944 -0.0812 0.0898 0.0105 newton_test(): Seek real roots of the Newton example x^3-2x-5=0. all_roots_in_xi = 0.4189 + 0.0000i -0.2095 + 0.2272i -0.2095 - 0.2272i evi = 0.4189 evi = -0.2095 + 0.2272i evi = -0.2095 - 0.2272i Interstitial interpolation error norm = 6.03961e-14 Number of roots = 1 Maximum residual at roots = 3.55271e-15 Exact real root : 2.094551481542328 Computed real root: 2.094551481542327 Exact f(roots) : 1.4210854715202e-14 Computed f(roots) : 3.552713678800501e-15 Error : 8.881784197001252e-16 jenkins_test(): Seek real roots of the Jenkins polynomial p(x) = x^4 + 5.6562x^3 + 5.8854x^2 + 7.3646x + 6.1354 all_roots_in_xi = 0.0018 + 0.2291i 0.0018 - 0.2291i -0.2000 + 0.0000i -0.9348 + 0.0000i evi = 0.0018 + 0.2291i evi = 0.0018 - 0.2291i evi = -0.2000 evi = -0.9348 Interstitial interpolation error norm = 6.82121e-13 Maximum residual at roots = 3.01981e-14 Number of roots = 2 Computed roots: -4.674054017161709 -0.999999999999996 Exact roots: -1.000000000000000 -4.674054017161709 f (Computed roots ): 1.0e-13 * -0.186517468137026 0.301980662698043 f(Exact roots): 1.0e-13 * -0.008881784197001 -0.186517468137026 cpr_test(): Normal end of execution. 25-Mar-2024 22:44:23