Question
Transcribed Text
A popular method for curve fitting is the βLeast Squaredβ method.
a) Determine the value of the constant k which best approximates a specified function f(x) on the
interval π β€ π₯ β€ π. Use as a cost function to be minimized:
πΏ(π) =
1
2
β« [π β π(π₯)]
2ππ₯
π
π
Verify that a minimum is achieved by checking the 2nd order optimality condition.
b) Determine the optimal value of π and πΏ(π) in fractional form for π(π₯) = π₯
2
, π = 0, πππ π = 1.
c) For the best linear fit, determine the optimal value of π, π πππ πΏ(π) in fractional form for π(π₯) =
π₯
2
, π = 0, πππ π = 1 where,
πΏ(π, π) =
1
2
β« [ππ₯ + π β π(π₯)]
2ππ₯
π
π
Hint: The answers to these problems can be confirmed using MATLABβs or Excelβs curve fitting.
In part a. we need to solve ππΏ(π)
ππ
= 0
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