Fri Mar 29 21:52:38 2024 zero_muller_test(): Python version: 3.10.12 Test zero_muller(), which uses Muller's method, with complex arithmeic, to solve a nonlinear equation. test01(): Demonstrate zero_muller() on F(X) = X*X+9. zero_muller(): Muller's root-finding method (complex root version) Iteration x_real x_imag ||fx|| ||disc|| -2 0.5000000000 0.5000000000 9.0138781887 -1 0.0000000000 1.0000000000 8.0000000000 0 1.0000000000 0.0000000000 10.0000000000 1 0.0000000000 -3.0000000000 0.0000000000 18.0000000000 zero_muller(): Absolute convergence of |F(X)|. X = 0.0 -3.0 with function value F(X): FX = 0.0 0.0 ||FX|| = 0.0 test02(): Demonstrate zero_muller() on F(X) = (X*X+4)*(X-10)*(X+20). zero_muller(): Muller's root-finding method (complex root version) Iteration x_real x_imag ||fx|| ||disc|| -2 0.5000000000 0.5000000000 786.3827391926 -1 0.0000000000 1.0000000000 603.7458074389 0 1.0000000000 0.0000000000 945.0000000000 1 0.0242802733 2.0507061379 46.6853784403 292576.8813244863 2 -0.0016499786 1.9990380412 1.5656742803 7255213.6000903565 3 -0.0000011428 2.0000011261 0.0013154356 2477.9662226890 4 0.0000000000 2.0000000000 0.0000000022 0.0000258907 zero_muller(): Absolute convergence of the X increment. X = 2.692886944105272e-12 2.000000000000209 with function value F(X): FX = -4.4751484971671e-11 -2.2141290278170117e-09 ||FX|| = 2.2145812351839962e-09 test03(): Demonstrate zero_muller() on Zhelyazkov's function. zero_muller(): Muller's root-finding method (complex root version) Iteration x_real x_imag ||fx|| ||disc|| -2 0.5000000000 0.5000000000 1.7780343017 -1 0.0000000000 1.0000000000 2.7212864609 0 1.0000000000 0.0000000000 1.1398341819 1 1.5705799215 -0.0000004486 0.0000012222 3.6964136697 2 1.5705798926 0.0000000000 0.0000000000 16.6875551235 zero_muller(): Absolute convergence of |F(X)|. X = 1.5705798925711434 6.711701927407336e-14 with function value F(X): FX = -1.2309597785531423e-13 1.8248958445237312e-13 ||FX|| = 2.2012511941565376e-13 zero_muller(): Muller's root-finding method (complex root version) Iteration x_real x_imag ||fx|| ||disc|| -2 -1.0000000000 2.0000000000 8.4140172656 -1 1.0000000000 2.0000000000 6.7016733534 0 0.0000000000 1.0000000000 2.7212864609 1 -0.5802520858 -0.0000000937 0.0000002667 118.2853729480 2 -0.5802520567 -0.0000000000 0.0000000000 128.4099686054 zero_muller(): Absolute convergence of the X increment. X = -0.5802520566719338 -1.7796326863841973e-15 with function value F(X): FX = -2.8248237082806327e-14 4.838780821845253e-15 ||FX|| = 2.8659670237605527e-14 zero_muller_test(): Normal end of execution. Fri Mar 29 21:52:38 2024