Dr' K' Gururajan, MCE, Hassan

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CURVE FITTING

Dr. M. SANKAR Professor and Head Department of
Mathematics Sapthagiri College of
Engineering Bangalore 560 057 Email
manisankarir_at_yahoo.com
Dr. M. SANKAR, SCE, Bangalore
Dr. K. Gururajan, MCE, Hassan
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Fitting a curve of the form

Dr. M. SANKAR, SCE, Bangalore
Dr. K. Gururajan, MCE, Hassan
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1. Discussion on fitting a curve of the form
Solution Consider the equation Taking logarithm
with respect to e on both sides,
Dr. M. SANKAR, SCE, Bangalore
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Putting , ,
we obtain . Thus, the
problem reduces to fitting a straight line.
Therefore, normal equations are and
Dr. M. SANKAR, SCE, Bangalore
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Fit a curve of the form for
the data given below
Solution First we
prepare the normal equations using which values
of a and b may be determined.
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Here, n 6
The normal equations are
and
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Thus, normal equations takes the form Solving
these equations for A and B yields A
0.3038 and B -0.02877.
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Since A logea and Blogeb, we have a eA
e0.3038 2.013 and b eB e- 0.02877
0.936. Thus, the required curve is

Dr. M. SANKAR, SCE, Bangalore
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2. Discussion on fitting a curve Consider
. First taking logarithms on either sides,
results in Choosing ,
, ,
Dr. M. SANKAR, SCE, Bangalore
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The problem now gets reduced to fitting a
straight line of the form Y A bX. The
respective normal equations are and

Dr. M. SANKAR, SCE, Bangalore
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Fit a power function (geometric curve) of the
form to the data given below.
Solution As discussed earlier, the normal
equations are

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Here, n 5
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Thus, normal equations are On solving these
two equations, we get
. Therefore,
. Thus, the least square
geometric curve is
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3. Discussion on fitting an exponential curve of
the form . We consider an
illustrative example. Consider .
Taking logarithm on either sides leads to
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Set and , above
expression reduces to . Thus,
normal equations are


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Normal equations may be written as
and If we solve this system
of linear equations, thus,
and
and . The required fit
is

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Thank You
Dr. M. SANKAR, SCE, Bangalore
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• Assignment problems
• Fit a curve of the form for the
  data
• 2. Fit a curve of the form for the
  data

Dr. M. SANKAR, SCE, Bangalore