Chapter 5 Interpolation Approximation Least Squares Regression Fall 2009

# Chapter 5 Interpolation Approximation Least Squares Regression Fall 2009

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Unformatted text preview: - 1 - Chapter 5 Interpolation, Approximation, and Least Squares Regression Contents Introduction ..................................................................................................................... - 2 - 5.1 Polynomials of Degree ࢔ .......................................................................................... - 3 - 5.2 Lagrange Interpolating Polynomials and Their Descendents ................................... - 4 - 5.2.1 Lagrange Polynomials ............................................................................... - 4 - 5.2.2 Neville's Algorithm and Barycentric Interpolation .................................... - 6 - 5.2.3 Chebyshev Polynomials and Lagrange-Chebyshev Interpolation ............. - 6 - Example 5.1 Lagrange and Lagrange-Chebyshev Interpolation ......................... - 8 - 5.3 Spline Interpolation ................................................................................................. - 10 - 5.3.1 Cubic Splines ........................................................................................... - 11 - 5.3.2 Equations for a Cubic Spline on ࢞૙, ࢞࢔ .................................................. - 11 - 5.3.3 Solving the Cubic Spline Equations ........................................................ - 13 - Example 5.2 Cubic Spline Interpolation ........................................................... - 14 - 5.4 The Least Squares Best Fit Polynomial .................................................................. - 15 - 5.4.1 Finding the Least Squares Best Fit Polynomial of Degree ࢔ ൌ ૚ ........... - 15 - Example 5.3 Least Squares for a 1 st Degree Polynomial .................................. - 18 - 5.4.2 General Polynomial Regression ............................................................... - 19 - Example 5.4 Least Squares for a 2 nd Degree Polynomial ................................. - 21 - 5.4.3 Polynomial Regression with User Defined Functions ............................. - 22 - Example 5.5 Polynomial Regression with User Defined Functions ................. - 22 - 5.5 Regression Statistics and the Coefficient of Determination, R 2 ............................. - 25 - 5.5.1 Definition of the Coefficient of Determination ....................................... - 25 - 5.5.2 Corrected versus Uncorrected Coefficient of Determination .................. - 27 - Example 5.6 Using the Coefficient of Determination to Discriminate between Models............................................................................................................... - 28 - Example 5.7 Interpolating in High Quality Data .............................................. - 30 - 5.6 Rules of Thumb for Interpolation and Approximation ........................................... - 31 - 5.7 Chapter Summary ................................................................................................... - 32 - Exercises ....................................................................................................................... - 32 -Exercises ....
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Chapter 5 Interpolation Approximation Least Squares Regression Fall 2009

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