ROOTFINDING
Regula Falsi Method
www.jesus-avalos.ucoz.com
ALGORITHM CODE:
RegulaFalsi[a0_,b0_,m_]:=Module[{},a=N[a0];b=N[b0]; c=(a*f[b]-b*f[a])/(f[b]-f[a]);k=0;
output={{k,a,c,b,f[c]}};
While[k<m, If[Sign[f[b]]==Sign[f[c]],b=c, a=c;];
c=(a*f[b]-b*f[a])/(f[b]-f[a]);
k=k+1;
output=Append[output,{k,a,c,b,f[c]}];];
Print[NumberForm[TableForm[output,TableHeadings->{None,{"k","ak","ck","bk","f[ck]"}}],16]];
Print[" c=",NumberForm[c,16]];
Print[" f[c]=",NumberForm[f[c],16]];]
EXAMPLE:
f[x_]=x^3-2x^2+3x/2
(3 x)/2-2 x2+x3
RegulaFalsi[-1,1,12]
{
{k, ak, ck, bk, f[ck]},
{0, -1., 0.8, 1., 0.432},
{1, -1., 0.6423357664233577, 0.8, 0.4033378536513656},
{2, -1., 0.5072408162536918, 0.6423357664233577, 0.3767843689852098},
{3, -1., 0.3907901518625014, 0.5072408162536918, 0.340431619474261},
{4, -1., 0.2929747128750934, 0.3907901518625014, 0.2929409494830454},
{5, -1., 0.2139490699474353, 0.2929747128750934, 0.2391685443454786},
{6, -1., 0.1526854897957456, 0.2139490699474353, 0.1859620523688113},
{7, -1., 0.1069412526417537, 0.1526854897957456, 0.1387620422415913},
{8, -1., 0.07382866194205702, 0.1069412526417537, 0.1002440660353247},
{9, -1., 0.0504288271173981, 0.07382866194205702, 0.07068535133336745},
{10, -1., 0.03418401370580981, 0.0504288271173981, 0.04897887259222585},
{11, -1., 0.02304895054924056, 0.03418401370580981, 0.03352316243099189},
{12, -1., 0.0154840093511178, 0.02304895054924056, 0.02275021729713151}
}
c= 0.0154840093511178
f[c]= 0.02275021729713151
Concise Program for the Regula Falsi
RegulaFalsi2[a0_,b0_,m_]:=Module[{},a=N[a0];b=N[b0];Ya=f[a];Yb=f[b];
c=(a*Yb-b*Ya)/(Yb-Ya); Yc=f[c]; k=0;While[k<m,
If[Sign[Yb]==Sign[Yc],
b=c;
Yb=Yc,
a=c;
Ya=Yc;];
c=(a*Yb-b*Ya)/(Yb-Ya);
Yc=f[c];
k=k+1;];
Print[" c=", NumberForm[c,11]];
Print["f[c]=", NumberForm[Yc,11]];]
EXAMPLE:
f[x_]=x^3-2x^2+3x/2
(3 x)/2-2 x2+x3
RegulaFalsi2[-1,1,12]
c= 0.015484009351
f[c]= 0.022750217297
Plot[(3 x)/2-2 x2+x3,{x,-1.,1.}]
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