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CS1371_14C_matrix_problems

# CS1371_14C_matrix_problems - COE1361 CS1371 Introduction to...

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1 9/22/03 COE1361 – CS1371 Introduction to Computing for Engineers Problem-solving with Matrices

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2 9/22/03 Vectors and Matrices Problems Background theory for some simple engineering problems Sample code Suggested problems to consider Learning Objectives Understand the nature of matrices Understand how to manipulate matrices in Matlab
3 9/22/03 Vectors and Matrices The purpose of this special set of notes is to introduce you to some common engineering applications of vectors and matrices. We’ll try to keep things at a very basic level but we may need to introduce some elementary background material to explain the problems… You’ll run into many interesting new problems as you move through the engineering curriculum!

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4 9/22/03 Fitting Polynomials to Data Fitting analytical curves to experimental data is a common task in engineering. The simplest is linear interpolation (straight lines between data points). Polynomials are often used to define curves, and there are several options: Fit curve through all data points ( polynomial interpolation ), Fit curve through some data points, Fit curve as close to points as possible ( polynomial regression , also called “least square fitting”) polynomial interpolation polynomial regression
5 9/22/03 Fitting Polynomial Through N Points A polynomial of degree N-1 contains N coefficients: To define these requires N constraints and these can be the requirement that the curve passes through N points: These can be written in matrix notation: 1 2 1 2 1 0 ( ) N N N N p x p x p x p x p - - - - = + + + + L 1 2 1 1 1 1 2 1 1 1 0 1 2 2 2 1 2 2 2 1 2 0 1 2 1 2 1 0 ( ) ( ) ( ) N N N N N N N N N N N N N N N N N y p x p x p x p x p y p x p x p x p x p y p x p x p x p x p - - - - - - - - - - - - = = + + + + = = + + + + = = + + + + L L M L 1 2 1 1 1 1 1 2 0 1 1 N N N N N N N N y x x p y x x p - - - - - = L M L M L y = X*p or: NOTE: This is called polynomial interpolation NOTE: This is called polynomial interpolation

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6 9/22/03 Fitting Polynomial Through N Points…
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CS1371_14C_matrix_problems - COE1361 CS1371 Introduction to...

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