) The Gaussian function occurs in many situations in scientific research. However, as it involves an exponential its computational cost can be burdensome in some applications. Thus, a polynomial approximation is sought. Assuming we want to use a least squares formulation with a cubic polynomial, answer the following questions: • Would this formulation lead to a linear or a nonlinear least squares problem? • List two algorithms you can use to solve this problem If you were given only two data points from the Gaussian curve to fit to, discuss what would happen to the solution process and quality. (i) Given the following data points provided, formulate and solve for the cubic polynomial curve of best fit. Show all working. 0.09 0.06 0.05 004 0.03 0.02 001 -1 08 06 04 02 02 04 0.6 a b.
) The Gaussian function occurs in many situations in scientific research. However, as it involves an exponential its computational cost can be burdensome in some applications. Thus, a polynomial approximation is sought. Assuming we want to use a least squares formulation with a cubic polynomial, answer the following questions: • Would this formulation lead to a linear or a nonlinear least squares problem? • List two algorithms you can use to solve this problem If you were given only two data points from the Gaussian curve to fit to, discuss what would happen to the solution process and quality. (i) Given the following data points provided, formulate and solve for the cubic polynomial curve of best fit. Show all working. 0.09 0.06 0.05 004 0.03 0.02 001 -1 08 06 04 02 02 04 0.6 a b.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:(1) The Gaussian function occurs in many situations in scientific research. However, as it involves an
exponential its computational cost can be burdensome in some applications. Thus, a polynomial
approximation is sought. Assuming we want to use a least squares formulation with a cubic
polynomial, answer the following questions:
Would this formulation lead to a linear or a nonlinear least squares problem?
• List two algorithms you can use to solve this problem
• If you were given only two data points from the Gaussian curve to fit to, discuss what would
happen to the solution process and quality.
(i) Given the following data points provided, formulate and solve for the cubic polynomial curve of
best fit. Show all working.
0.09
0.08
0.07
0.06
0.05
b
0.04
0.03
0.02
0.01
-1
0.8
0.6
04 02
0.2
0.4
0.6
a
-0.6000
-0.2000
0.1000
0.5000
a
b 8.6517e-3 6.3928e-2 7.7111e-2 1.721e-2
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