2 3 decimal

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Bisection root-finding method.
reference function for Bisection() 1 f a b epsilon maxIters Bisection.ref i 0 : P1 a : P2 b : i maxIters < P3 P1 P2 + 2 / : P3 f abs epsilon < break P1 f P3 f * sign 0 > P1 P3 : P2 P3 : if i i 1 + : 21 line if 21 line while i maxIters ≡ max number of steps exceeded error P3 i 11 mat 21 mat if 51 line :

function used for testing (references: http://www.m-hikari.com/ams/ams-2010/ams-13-16-2010/gottliebAMS13-16-2010.pdf)

a f1 3 a sin * 2 - :

epsilon 105 -^:

a f2 a e a^* 1 - :

a f3 11 a 11^* 1 - :

iterations 100 :

a f4 e a 2^7 a * + 30 -^1 - :

a f5 1 a / a sin - 1 + :

a f6 a 3^2 a * - 5 - :

a f7 1 a / 1 - :

a f0 a f1 a f2 21 sys :

x f2

ε.fx 105 -^:

ε.ΔB 103 -^:

Ε ε.fx ε.ΔB 21 sys :

Bound_P1 5 :

Bound_P2 20 - :

x f2 Bound_P1 Bound_P2 epsilon 1 Bisection 0.5671 2011 mat 21 mat

x f2 Bound_P1 Bound_P2 ε.fx ε.ΔB 21 mat 1 Bisection 0.5666 1511 mat 21 mat

x f2 Bound_P1 Bound_P2 ε.fx ε.ΔB 21 sys 1 Bisection 0.5666 1511 mat 21 mat

x f2 Bound_P1 Bound_P2 ε.fx ε.ΔB 12 mat 1 Bisection 0.5666 1511 mat 21 mat

x f2 Bound_P1 Bound_P2 Ε 1 Bisection 0.5666 1511 mat 21 mat

x f2 Bound_P1 Bound_P2 epsilon iterations Bisection.ref 0.5671 2011 mat 21 mat

x# f2 1 epsilon iterations 1 Broyden 0.5671 1011 mat 21 mat

x f2 Bound_P1 Bound_P2 epsilon iterations Bisection 0.5671 2011 mat 21 mat

x f2 Bound_P1 Bound_P2 epsilon iterations Bisection.ref 0.5671 2011 mat 21 mat

x f2 Bound_P1 Bound_P2 epsilon 1 Bisection 0.5671 2011 mat 21 mat

x f0

Bound_P1 0.1 :

Bound_P2 2.1 :

same bounds for all functions

x f0 Bound_P1 Bound_P2 epsilon 1 Bisection 0.7297 1511 mat 21 mat 0.5671 1711 mat 21 mat 21 mat

Bound_P1 01 - 21 sys :

Bound_P2 2.2 2.5 21 sys :

custom bounds

a f1 b f2 21 sys Bound_P1 Bound_P2 epsilon 1 Bisection 0.7297 1411 mat 21 mat 0.5671 1811 mat 21 mat 21 mat

x# 1 el f1 x# 2 el f2 21 sys Bound_P1 epsilon iterations 1 Broyden 0.7297 0.5671 21 sys 811 mat 21 mat