13 March 2018 1:01:49.458 PM ZOOMIN_PRB FORTRAN90 version Test the ZOOMIN library. TEST01: (Polynomial function F(X)) Find a root of F(X)=(X+3)*(X+3)*(X-2)=0 ZOOMIN A compilation of scalar zero finders, based on the work of Joseph Traub. 1 point formulas use: x1 = 1.50000 fx1= -10.1250 2 point formulas add: x2 = 4.00000 fx2= 98.0000 3 point formulas add: x3 = 1.00000 fx3= -16.0000 User estimated multiplicity = 1 Polynomial degree = 3 Highest derivative supplied = 3 Error tolerance = 0.100000E-04 Maximum number of steps = 30 Newton method substep parameter = 3 Technique Root Steps Error Multiplicity 1. One point iteration functions with memory: Secant 2.00000 6 Extended secant 2.00000 5 Capital Phi(2,1) 2.00000 4 R8_Muller 2.00000 4 Perp E(2,1) 2.00000 5 Star E(2,1) 2.00000 4 Finite difference Halley 2.00000 3 Phi(1,2) 2.00000 3 Perp E(1,2) 2.00000 3 Star E(1,2) 2.00000 3 Dagger E(1,2) 2.00000 3 2. One point iteration functions. Newton 2.00000 4 Steffenson -3.00086 24 Stirling 2.00000 24 midpoint 2.00000 3 Traub-Ostrowski 2.00000 2 Chebyshev 2.00000 3 Halley Super 2.00000 2 Whittaker 2.00000 5 Whittaker2 2.00000 3 E3 2.00000 3 E4 2.00000 3 Halley 2.00000 3 Psi(2,1) 2.00000 2 Psi(1,2) 2.00000 3 Capital Phi(0,3) 2.00000 2 Reduced Capital Phi(0,4) 2.00000 2 Ostrowski square root 2.00000 2 Euler 2.00000 2 Laguerre 2.00000 1 3. Multipoint iteration functions. Traub first 2.00000 4 Traub second 2.00000 2 Traub twelfth 2.00000 3 Traub thirteenth 2.00000 2 Modified Newton, NSUB= 3 2.00000 7 Traub fourth, NSUB= 3 2.00000 6 Newton - secant 2.00000 3 Traub sixth 2.00000 3 Traub seventh 2.00000 3 Traub eighth 2.00000 3 Traub ninth 2.00000 2 Traub type 1, form 10 2.00000 3 Traub type 1, form 11 2.00000 3 Traub fourteenth 2.00000 2 Traub fifteenth 2.00000 2 Traub sixteenth 2.00000 2 King, BETA=0 2.00000 2 King, BETA=1 2.00000 2 King, BETA=2 2.00000 3 Jarratt 2.00000 2 Jarratt inverse-free 2.00000 3 4. Multiple root methods, multiplicity given. Script E2 2.00000 4 Script E3 2.00000 3 Script E4 2.00000 3 Star E 1,1(f) 2.00000 6 5. Multiple root methods, multiplicity not given. E2(U) 2.00000 4 1.00002 Phi 1,1(U) 2.00000 3 1.00000 Traub third 2.00000 4 1.00000 Van de Vel 2.00000 2 1.00301 Improved Van de Vel 2.00000 4 1.00000 6. Bisection methods Bisection 2.00000 22 Regula falsi 4.00000 31 2 Brent 2.00000 7 Bisection + secant 2.00000 15 Bisection + secant + inv quad 2.00000 5 TEST02: (Nonpolynomial function F(X)) Find a root of F(X) = COS(X) - X ZOOMIN A compilation of scalar zero finders, based on the work of Joseph Traub. 1 point formulas use: x1 = 0.900000 fx1= -0.278390 2 point formulas add: x2 = 0.400000 fx2= 0.521061 3 point formulas add: x3 = 0.500000 fx3= 0.377583 User estimated multiplicity = 1 The function is not known to be polynomial. Highest derivative supplied = 3 Error tolerance = 0.100000E-04 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) is misbehaving. 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 0.739090 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 2 Euler is misbehaving. 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 0.739090 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 1.00000 Phi 1,1(U) 0.739090 1 1.00000 Traub third 0.739090 2 1.00000 Van de Vel 0.739085 2 1.00000 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_PRB Normal end of execution. 13 March 2018 1:01:49.459 PM