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Faculty of Applied Engineering and Urban Planning

Faculty of Applied Engineering and Urban Planning. Civil Engineering Department. Numerical Analysis. Curve Fitting. Lecture 13 Week 11. 2 nd Semester 2007/2008. From Dr. Arafa Lecture Notes. From Dr. Arafa Lecture Notes. From Dr. Arafa Lecture Notes. Interpolation VS. Curve Fitting.

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Faculty of Applied Engineering and Urban Planning

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  1. Faculty of Applied Engineering and Urban Planning Civil Engineering Department Numerical Analysis Curve Fitting Lecture 13 Week 11 2nd Semester 2007/2008

  2. From Dr. Arafa Lecture Notes

  3. From Dr. Arafa Lecture Notes

  4. From Dr. Arafa Lecture Notes

  5. Interpolation VS. Curve Fitting

  6. Definition • Interpolation is the process of finding equations to approximate straight lines and curves that best fit given sets of data. • Curve Fitting is the process of finding the dependent variable from some data of the independent variable . Regression can be linear (straight line) or curved (quadratic, cubic, etc.)

  7. Straight Line Fit: A Polynomial Function of First Degree If there is some theoretical basis on which we believe the relationship between the two variables to be: we should set up the following system of equations from the collection of many experimental data:

  8. Straight Line Fit: A Polynomial Function of First Degree This system can be written as: And solved using the following formula:

  9. Straight Line Fit: A Polynomial Function of First Degree Solving the previous system leads to the following equation:

  10. From Dr. Arafa Lecture Notes

  11. From Dr. Arafa Lecture Notes

  12. From Dr. Arafa Lecture Notes

  13. From Dr. Arafa Lecture Notes

  14. From Dr. Arafa Lecture Notes

  15. From Dr. Arafa Lecture Notes

  16. From Dr. Arafa Lecture Notes

  17. Questions?

  18. Linearization Consider the following equation:

  19. Group Work

  20. Questions?

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