Interpolation and Curve Fitting
Interpolation and Curve Fitting
Interpolation and Curve Fitting
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Sensitivity <strong>and</strong> Conditioning<br />
• Sensitivity of least squares solution to Aa≈b<br />
depends on b as well as A<br />
• Define angle θbetween b <strong>and</strong> y = Aa by<br />
y<br />
cos( )<br />
<br />
b<br />
• Bound on perturbation ∆x in solution x due to<br />
perturbation ∆b in b is given by<br />
x<br />
x<br />
2<br />
2<br />
2<br />
2<br />
cond<br />
( A)<br />
Aa<br />
<br />
b<br />
1<br />
cos(<br />
2<br />
2<br />
)<br />
b<br />
2<br />
Numerical Methods © Wen-Chieh Lin 47<br />
b<br />
2
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