View source for Non-precise data/Fig4

<center><asy>
int M=30;
real a = 0.07;
real a0 = 0.15;
real b = 0.02;
real c = 0.6;
real d = -0.2;

real x0 = -0.22;
real u = 0.2;
real v = 0.32;

draw ((-0.7,0)--(0.3,0),Arrow);
draw ((x0,-0.02)--(x0,1.2),Arrow);

label("$x$",(0.3,0),E);
label(rotate(90)*"$y$",(x0,1.2),N);
label("$x_0$",(x0,-0.02),S);

guide g1; guide g2; guide g3; guide g4; guide g5;
for (int k=floor(-0.7M); k<floor(0.3M); ++k) {
  real x = k/M;
  real z = 1+3*x^2;
  real y1 = 1/(z-2a-a0)+2b*(1+c*x)+d;
  real y2 = 1/(z-a-a0)+b*(1+c*x)+d;
  real y3 = 1/(z-a0)+d;
  real y4 = 1/(z+a-a0)-b*(1+c*x)+d;
  real y5 = 1/(z+2a-a0)-2b*(1+c*x)+d;
  g1=g1..(x,y1);
  g2=g2..(x,y2);
  g3=g3..(x,y3);
  g4=g4..(x,y4);
  g5=g5..(x,y5);
}
draw(g1,defaultpen+1);
draw(g2,defaultpen+1);
draw(g3,defaultpen+1);
draw(g4,defaultpen+1);
draw(g5,defaultpen+1);

real x = x0;
real z = 1+3*x^2;
real y1 = 1/(z-2a-a0)+2b*(1+c*x)+d;
real y2 = 1/(z-a-a0)+b*(1+c*x)+d;
real y3 = 1/(z-a0)+d;
real y4 = 1/(z+a-a0)-b*(1+c*x)+d;
real y5 = 1/(z+2a-a0)-2b*(1+c*x)+d;
path g = (x,y1)..(x-u,y2)..(x-v,y3)..(x-u,y4)..(x,y5);
draw( g );

pair w = (0.1,-0.6);

pair p = point(g,0.5);
dot ( p );
draw( p--p-0.5w, dashed );
label(rotate(90)*"$\Psi_{x_0}(y)$",p-0.5w,N);

draw( (x,y2)--(x-u,y2) );
draw( (x,y3)--(x-v,y3) );
draw( (x,y4)--(x-u,y4) );

draw( (x-u,y2+0.05)--(x-u,y4-0.05) );
draw( (x-v,y2+0.1)--(x-v,y4-0.1) );

real x = -0.15;
real z = 1+3*x^2;
real y4 = 1/(z+a-a0)-b*(1+c*x)+d;
dot( (x,y4) );
draw( (x,y4)--(x,y4)+w, dashed );
label("$\scriptstyle \underline f_\alpha(x)$",(x,y4)+w,SE);

real x = -0.05;
real z = 1+3*x^2;
real y3 = 1/(z-a0)+d;
dot( (x,y3) );
draw( (x,y3)--(x,y3)+w, dashed );
label("$\scriptstyle \underline f_1(x)=\overline f_1(x)$",(x,y3)+w,SE);

real x = 0.05;
real z = 1+3*x^2;
real y2 = 1/(z-a-a0)+b*(1+c*x)+d;
dot( (x,y2) );
draw( (x,y2)--(x,y2)+w, dashed );
label("$\scriptstyle \overline f_\alpha(x)$",(x,y2)+w,SE);

label("\small Fig. a4: Non-precise function",(x0,-0.2));

shipout(scale(250,120)*currentpicture);
</asy></center>