, , , MATLAB polyfit, . :
q=polyfit(x,y,n)
y ; x ; n ; p n+1.
x=[1 2 3 4 4 5 3 6 10 8 9 7];
:
y=[2 2.5 2 4 4.5 5 4 5 9 7 8 7];
polyfit n=1, n=2 n=3:
>> x=[1 2 3 4 4 5 3 6 10 8 9 7];
>> y=[2 2.5 2 4 4.5 5 4 5 9 7 8 7];
>> p1=polyfit(x,y,1)
p1 =
0.7918 0.9089
>> p2=polyfit(x,y,2)
p2 =
0.0107 0.6724 1.1593
>> p3=polyfit(x,y,3)
p3 =
-0.0017 0.0392 0.5421 1.3132
p1, p2, p3, , , . , , , .. . 2.24.1 ( polyval):
>> x=[1 2 3 4 4 5 3 6 10 8 9 7];
>> y=[2 2.5 2 4 4.5 5 4 5 9 7 8 7];
>> title(' ')
>> xlabel('x'); ylabel('y'); hold on
>> plot(x,y,'ko')
>> p1=polyfit(x,y,1);
>> p2=polyfit(x,y,2);
>> p3=polyfit(x,y,3);
>> t=0:0.05:10;
>> y1=polyval(p1,t);
>> y2=polyval(p2,t);
>> y3=polyval(p3,t);
>> plot(t,y1,'k-',t,y2,'k--',t,y3,'k:'), grid on
>> legend(' ',...
' ',...
' ',...
' ',2)
, . , .
.
. , , , .. ( , , , .. ). , (.. ), . ( ), ( ), .. , , , .
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. 2.24.1. .
. 2.24.2. .
spline, :
yy=spline(x,y,xx)
y, , x yy, , xx.
, , , x y, . 2.24.2.
>> x=[1 2 3 4 5 6 7 8 9 10 11 12];
>> y=[2 3 6 4.5 7 7.5 9 8 10 11 5 1];
>> title(' ');
>> xx=0:0.05:12;
>> yy=spline(x,y,xx);
>> xlabel('x'); ylabel('y');
>> plot(x,y,'ko',xx,yy,'k-'), grid on;
>> legend(' ',' ')
(-) MATLAB interp1, :
yy=interp1(x,y,xx,method)
x ; y ; xx , , yy; method , ( , ).
interp1 :
'nearest' ( ());
'linear' ( ) ;
'spline' ;
'pchip' 'cubic' .
'spline' , , .
'pchip' . , 'pchip', , , .
'spline', 'pchip'.
, , , , interp1 ( . 2.24.3).
. 2.24.3. .
MATLAB , ( interp2), ( interp3) ( interpn) .
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5.