DOPbox
Discrete Orthogonal Polynomial Toolbox
Getting Started
Matthew Harker and Paul O’Leary
Institute for Automation
University of Leoben
A-8700 Leoben,Austria
URL: automation.unileoben.ac.at
Original: January 9, 2013
c
2013
Last Modified: June 3, 2013
Contents
1 Toolbox description 2
2 Toolbox Functions 2
2.1 Generate a set of nodes – dopNodes.m . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Generate a set of discrete orthogonal polynomials – dop.m . . . . . . . . . . . . . 6
2.2.1 Properties of the Basis functions . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.2 Generating complex basis functions . . . . . . . . . . . . . . . . . . . . . . 8
2.2.3 Using dop.m to compute a regularizing differential operator. . . . . . . . . 11
2.3 Generate a matrix D
L
to perform local d erivative app roximation – dopDiffLocal
.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4 Apply a set of constraints to a set of basis functions – dopConstrain.m . . . . . 17
2.5 Global and local polynomial approximation – dopApproxLocal.m . . . . . . . . . 20
2.6 Interpolating using basis functions – dopInterpolate.m . . . . . . . . . . . . . . 25
2.7 Generate a set sine basis functions – dopSine.m . . . . . . . . . . . . . . . . . . . 26
2.8 Discrete Weighted Orthogonal Polynomials: dopWeightBasis . . . . . . . . . . . 27
2.9 Weighted regression with weighted basis functions . . . . . . . . . . . . . . . . . . 28
2.10 dopFit and dopVal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.10.1 Fitting a high degree polynomials . . . . . . . . . . . . . . . . . . . . . . . 29
2.10.2 High degree polynomial expansion . . . . . . . . . . . . . . . . . . . . . . . 32
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