Ch-5 computational method 2022 Interpolation and curve

Outline:
1. Introduction
2. Curve fitting
2.1 Least –Square regression
 Linear regression
 Polynomial regression
 Multiple regression
2.2 Interpolation
 Newton’s Divided –Difference
 Interpolating polynomial
 Lagrange interpolating polynomial
 Cubic Spline Interpolation
Computational Methods
(EPCE 2204)
Credit: 3 Hrs (Lecture: 2 Hr & Lab: 3 Hr)
__________________________________________
Chapter-Five
Interpolation and Approximation
Tamiru Getahun (MSc)
ASTU

What is curve fitting and why we study it?
• Curve fitting refers to finding an appropriate mathematical model that expresses the relationship between
a dependent variable Y and a single independent variable X and estimating the values of its parameters using
Linear or nonlinear regression.
• Two types of curve fitting
I. Least square regression
• Given data for discrete values, derive a single curve that represents the general trend of the data.
• When the given data exhibit a significant degree of error or noise.
II. Interpolation
• Given data for discrete values, fit a curve or a series of curves that pass directly through each of the points.
• When data are very precise.
Tamiru G. G. (MSc) tamiru.getahun@astu.edu.et
ASTU – EPCE Dpt 2
• Data are often given for discrete values along a continuum. However, you may require estimates
at points between the discrete values. (x0,y0), (x1,y1),………………….,(xn,yn)

5.1 Least Square Regression
1. Simple Linear Regression
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5.2 polynomial Interpolation

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Ch-5 computational method 2022 Interpolation and curve

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