Functions
close all define function and intervals syms x	f (x)

	fplot (f,[a, b])

	axis ([a, b,-1, 2]) hold on plot([a

f	char ()

	xlabel ("x") legend("f(x)") %% fnum

	fprintf ('Equation to solve:%s=0. \n', char(f))

	disp (['mid point:Approximate root:', num2str(rootApprox)])

	fprintf ('mid point:root:%f after %i iterations. \n', rootApprox(end), length(rootApprox))

	fprintf ('linear:root:%f after %i iterations. \n', rootLinear(end), length(rootLinear))

	fprintf ('quad:root:%f after %i iterations. \n', rootQuad(end), length(rootQuad))

Evaluate the function at the approximate root and plot the result	semilogy (rootApprox, f_val, ' *b', 'MarkerSize', 10)

	semilogy (abs(rootApprox-rootApprox(end)), '- *m', 'MarkerSize', 10)

hold on	semilogy (max(eps/10, abs(rootLinear-rootLinear(end))), '- *b', 'MarkerSize', 10)

	semilogy (max(eps/10, abs(rootQuad-rootQuad(end))), '-or', 'MarkerSize', 10)

	title ("Iteration history")

	xlabel ("iteration k")

	ylabel ("\|x^\ast-x_k\|") legend("midpoint"

guarantee entry into the loop while	abs (fc) >

	if (1==method &&(-fa/fb >TFAC\|\|-fb/fa >TFAC) &&length(xvec)< 4) % improve linear method_loc=0

	fprintf ('switch method to bisect at[%f, %f]\n', a, b)

if	~isempty (cr) c

else	disp ("no root found") end otherwise disp("Unknown method! Choose from [0

end if	subs (func, x, midpoint)

elseif	subs (func, x, a) *subs(func

Variables
	clear

	clc

	a = 0.01

	b = 2

graphics	f0 =figure()

Define the tolerance for the bisection	method

Call the bisection method to find the root of the function	f

Call the bisection method to find the root of the function	eps

Call the bisection method to find the root of the function	false

	rootApprox = Bisect(fnum, a, b, eps, 0)

Linear improved bisection	rootLinear = Bisect(fnum, a, b, eps, true)

	rootQuad = Bisect(fnum, a, b, eps, 2)

	f3 =figure()

	linear

	quadratic

grid	on

function	xvec

	fc = 2*eps

	fb =func(b)

	method_loc = method

	TFAC =2

end switch method_loc case midpoint	c = (a + b) / 2

	dd =[1 a a^2

	cr = getRoot(dd,a,b)

Exact root found	break

elseif fa fc< 0 b=c;% Root is in the left half else a=c;% Root is in the right half end xvec=[xvec, c];% Store the midpointendend%%function r=getRoot(dd, a, b) r=roots(dd(end:-1:1));r=r(a<=r &r<=b);if length(r)==2 disp("!! 2 roots !!") endend%%function Visualize_Interval_subdivision(func, a, b)%fa=func(a);fb=func(b);c0=(a+b)/2;% midpointc1=a-(b-a) fa/(fb-fa);% linear% c2=c0;% quadratic via midpointc2=c1;% quadratic via lineardd=[1 a a^2;1 b b^2;1 c2 c2^2]\[fa;fb;double(func(c2))];cr=getRoot(dd, a, b);if ~isempty(cr) c2=cr(1);else disp("no root found") endfigure() plot([a, b], [fa, fb], 'sg') hold onplot(c0, func(c0),' *m') plot(c1, func(c1), 'db') plot(c2, func(c2), 'or')%x=linspace(a, b, 101);plot(x, func(x),'-g') plot([a, b], [fa, fb],'-b') y=polyval(dd(end:-1:1), x);plot(x, y,'-r') plot([a, b], [0, 0],'-k') title("Visualize 3 strategies in bisection step") legend("given data","midpoint","linear","quadratic") end%%function xvec=Bisect_org(func, a, b, eps, linear)% Initialize the bisection method:Co-pilotxvec=[];while(b - a)/2 > eps if linear	midpoint = double(a-(b-a)*func(a)/(func(b)-func(a)))

elseif	x

Function Documentation

◆ abs()

guarantee entry into the loop while abs ( fc )

Here is the caller graph for this function:

◆ axis()

axis ( )

◆ char()

f char ( )

virtual

Here is the caller graph for this function:

◆ disp() [1/2]

else disp ( "no root found" )

◆ disp() [2/2]

disp ( )

◆ f()

close all define function and intervals syms x f ( x )

◆ fplot()

fplot ( f )

◆ fprintf() [1/5]

fprintf	(	'Equation to solve:%	s = `0. \n'`,
		char(f)
	)

◆ fprintf() [2/5]

fprintf	(	'linear:root:%f after %i iterations. \n'	,
		rootLinear(end)	,
		length(rootLinear)
	)

◆ fprintf() [3/5]

fprintf	(	'mid point:root:%f after %i iterations. \n'	,
		rootApprox(end)	,
		length(rootApprox)
	)

◆ fprintf() [4/5]

fprintf	(	'quad:root:%f after %i iterations. \n'	,
		rootQuad(end)	,
		length(rootQuad)
	)

◆ fprintf() [5/5]

fprintf	(	'switch method to bisect at\n'	[%f, %f],
		a	,
		b
	)

◆ if()

if ( )

pure virtual

◆ semilogy() [1/4]

semilogy	(	abs(rootApprox-rootApprox(end))	,
		'- *m'	,
		'MarkerSize'	,
		10
	)

◆ semilogy() [2/4]

hold on semilogy	(	max(eps/10, abs(rootLinear-rootLinear(end)))	,
		'- *b'	,
		'MarkerSize'	,
		10
	)

◆ semilogy() [3/4]

semilogy	(	max(eps/10, abs(rootQuad-rootQuad(end)))	,
		'-or'	,
		'MarkerSize'	,
		10
	)

◆ semilogy() [4/4]

Evaluate the function at the approximate root and plot the result semilogy	(	rootApprox	,
		f_val	,
		' *b'	,
		'MarkerSize'	,
		10
	)

◆ subs() [1/2]

elseif subs	(	func	,
		x	,
		a
	)

◆ subs() [2/2]

end if subs	(	func	,
		x	,
		midpoint
	)

◆ title()

title ( "Iteration history" )

◆ xlabel() [1/2]

xlabel ( "iteration k" )

◆ xlabel() [2/2]

xlabel ( "x" )

◆ ylabel()

ylabel ( "|x^\ast-x_k|" )

◆ ~isempty()

if ~isempty ( cr )

Variable Documentation

◆ a

Call the bisection method to find the root of the function a = 0.01

Definition at line 6 of file bisect_vis.m.

◆ b

b b = 2

Definition at line 6 of file bisect_vis.m.

◆ break

Exact root found break

Definition at line 100 of file bisect_vis.m.

◆ c

c c = (a + b) / 2

Definition at line 81 of file bisect_vis.m.

◆ clc

clc

Definition at line 2 of file bisect_vis.m.

◆ clear

clear

Definition at line 2 of file bisect_vis.m.

◆ cr

cr = getRoot(dd,a,b)

Definition at line 87 of file bisect_vis.m.

◆ dd

dd =[1 a a^2

Definition at line 86 of file bisect_vis.m.

◆ eps

Call the bisection method to find the root of the function eps

Definition at line 31 of file bisect_vis.m.

◆ f

Call the bisection method to find the root of the function f

Definition at line 30 of file bisect_vis.m.

◆ f0

graphics f0 =figure()

Definition at line 17 of file bisect_vis.m.

◆ f3

f3 =figure()

Definition at line 49 of file bisect_vis.m.

◆ false

Call the bisection method to find the root of the function false

Definition at line 31 of file bisect_vis.m.

◆ fb

fb =func(b)

Definition at line 72 of file bisect_vis.m.

◆ fc

else end fc = 2*eps

Definition at line 67 of file bisect_vis.m.

◆ linear

linear

Definition at line 58 of file bisect_vis.m.

◆ method

Define the tolerance for the bisection method

Definition at line 28 of file bisect_vis.m.

◆ method_loc

method_loc = method

Definition at line 73 of file bisect_vis.m.

◆ midpoint

else midpoint = double(a-(b-a)*func(a)/(func(b)-func(a)))

Definition at line 160 of file bisect_vis.m.

◆ on

grid on

Definition at line 59 of file bisect_vis.m.

◆ quadratic

quadratic