16-May-2024 08:10:21 zoomin_test( MATLAB/Octave version 6.4.0 Test zoomin(). test01(): Seek a root of a polynomial function F(X). F(X) = (X+3) * (X+3) * (X-2) zoomin_all_test(): A compilation of scalar zero finders, based on the work of Joseph Traub. 1 point formulas use: x1 = 1.5 fx1= -10.125 2 point formulas add: x2 = 4 fx2= 98 3 point formulas add: x3 = 1 fx3= -16 User estimated multiplicity = 1 Polynomial degree = 3 Highest derivative supplied = 3 Error tolerance = 1e-05 Maximum number of steps = 30 Newton method substep parameter = 3 Technique Root Steps Error Multiplicity 1. One point iteration functions with memory: Secant 2 6 Extended secant 2 5 Capital Phi(2,1) 2 4 R8_Muller 2 4 Perp E(2,1) 2 5 Star E(2,1) 2 4 Finite difference Halley 2 3 Phi(1,2) 2 3 Perp E(1,2) 2 3 Star E(1,2) 2 3 Dagger E(1,2) 2 3 2. One point iteration functions. Newton 2 4 Steffenson -3.00086 24 Stirling 2 24 midpoint 2 3 Traub-Ostrowski 2 2 Chebyshev 2 3 Halley Super 2 2 Whittaker 2 5 Whittaker2 2 3 E3 2 3 E4 2 3 Halley 2 3 Psi(2,1) 2 2 Psi(1,2) 2 3 Capital Phi(0,3) 2 2 Reduced Capital Phi(0,4) 2 2 Ostrowski square root 2 2 Euler 2 2 Laguerre 2 1 3. Multipoint iteration functions. Traub first 2 4 Traub second 2 2 Traub twelfth 2 3 Traub thirteenth 2 2 Modified Newton, NSUB = 3 2 7 Traub fourth, NSUB = 3 2 6 Newton - secant 2 3 Traub sixth 2 3 Traub seventh 2 3 Traub eighth 2 3 Traub ninth 2 2 Traub type 1, form 10 2 3 Traub type 1, form 11 2 3 Traub fourteenth 2 2 Traub fifteenth 2 2 Traub sixteenth 2 2 King, BETA=0 2 2 King, BETA=1 2 2 King, BETA=2 2 3 Jarratt 2 2 Jarratt inverse-free 2 3 4. Multiple root methods, multiplicity given. Script E2 2 4 Script E3 2 3 Script E4 2 3 Star E 1,1(f) 2 6 5. Multiple root methods, multiplicity not given. E2(U) 2 4 1.00002 Phi 1,1(U) 2 3 1 Traub third 2 4 1 Van de Vel 2 2 1.00301 Improved Van de Vel 2 4 1 6. Bisection methods Bisection 2 22 Regula falsi 2 6 Brent 2 7 Bisection + secant 2 15 Bisection + secant + inv quad 2 5 test02(): Nonpolynomial function F(X) Find a root of F(X) = COS(X) - X zoomin_all_test(): A compilation of scalar zero finders, based on the work of Joseph Traub. 1 point formulas use: x1 = 0.9 fx1= -0.27839 2 point formulas add: x2 = 0.4 fx2= 0.521061 3 point formulas add: x3 = 0.5 fx3= 0.377583 User estimated multiplicity = 1 The function is not known to be polynomial. Highest derivative supplied = 3 Error tolerance = 1e-05 Maximum number of steps = 60 Newton method substep parameter = 3 Technique Root Steps Error Multiplicity 1. One point iteration functions with memory: Secant 0.739086 3 Extended secant 0.739085 3 Capital Phi(2,1) -4.09833e+40 13 error= 4 R8_Muller 0.739082 2 Perp E(2,1) 0.739085 3 Star E(2,1) 0.739085 3 Finite difference Halley 0.739084 2 Phi(1,2) 0.739085 2 Perp E(1,2) 0.739085 2 Star E(1,2) 0.739085 2 Dagger E(1,2) 0.739085 2 2. One point iteration functions. Newton 0.73909 2 Steffenson 0.739083 2 Stirling 0.739085 3 midpoint 0.739085 2 Traub-Ostrowski 0.739085 2 Chebyshev 0.739085 2 Halley Super 0.739085 2 Whittaker 0.739085 3 Whittaker2 0.739085 2 E3 0.739085 2 E4 0.739085 2 Halley 0.739085 2 Psi(2,1) 0.739085 2 Psi(1,2) 0.739085 2 Capital Phi(0,3) 0.739085 2 Reduced Capital Phi(0,4) 0.739084 1 Ostrowski square root 1575.04 61 error= 2 Euler -5.8012e+06 61 error= 2 3. Multipoint iteration functions. Traub first 0.739079 2 Traub second 0.739085 2 Traub twelfth 0.739085 2 Traub thirteenth 0.739085 2 Modified Newton, NSUB = 3 0.739085 4 Traub fourth, NSUB = 3 0.739085 4 Newton - secant 0.739085 2 Traub sixth 0.739085 2 Traub seventh 0.739085 2 Traub eighth 0.739085 2 Traub ninth 0.739085 2 Traub type 1, form 10 0.739085 2 Traub type 1, form 11 0.739085 2 Traub fourteenth 0.739087 1 Traub fifteenth 0.739084 1 Traub sixteenth 0.739085 2 King, BETA=0 0.739085 2 King, BETA=1 0.739085 2 King, BETA=2 0.739085 2 Jarratt 0.739085 2 Jarratt inverse-free 0.739085 2 4. Multiple root methods, multiplicity given. Script E2 0.73909 2 Script E3 0.739085 2 Script E4 0.739085 2 Star E 1,1(f) 0.739086 3 5. Multiple root methods, multiplicity not given. E2(U) 0.739089 2 1 Phi 1,1(U) 0.73909 1 1 Traub third 0.73909 2 1 Van de Vel 0.739085 2 1 Improved Van de Vel 0.739085 2 1.00102 6. Bisection methods Bisection 0.739081 14 Regula falsi 0.739085 4 Brent 0.739082 5 Bisection + secant 0.739086 3 Bisection + secant + inv quad 0.739085 3 zoomin_test(): Normal end of execution. 16-May-2024 08:10:21