First Semester in Numerical Analysis with Julia, 2020a

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CHAPTER 5. APPROXIMATION THEORY 215 plot(xaxis,map(x->e^x,xaxis),label=L"e^x") plot(xaxis,cheb2,label="Chebyshev least squares poly of degree 2") plot(xaxis,leg2,label="Legendre least squares poly of degree 2") legend(loc="upper left"); In the following, we compare second degree least squares polynomial approximations for f(x) =e x2 . Compare how good the Legendre and Chebyshev polynomial approximations are in the midinterval and toward the endpoints. In [19]: f(x)=e^(x^2) xaxis=-1:1/100:1 polyChebCoeff(x->f(x),2) cheb2=map(x->polyCheb(x,2),xaxis) polyLegCoeff(x->f(x),2) leg2=map(x->polyLeg(x,2),xaxis) plot(xaxis,map(x->f(x),xaxis),label=L"e^{x^2}") plot(xaxis,cheb2,label="Chebyshev least squares poly of degree 2") plot(xaxis,leg2,label="Legendre least squares poly of degree 2") legend(loc="upper center");
CHAPTER 5. APPROXIMATION THEORY 216 Exercise 5.3-3: Use Julia to compute the least squares polynomial approximations P 2 (x),P 4 (x),P 6 (x) to sin 4x using Chebyshev basis polynomials. Plot the polynomials together with sin 4x.
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First Semester in Numerical Analysi
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First Semester in Numerical Analysi
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Contents 1 Introduction 5 1.1 Revie
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Preface This book is based on my le
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Chapter 1 Introduction 1.1 Review o
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CHAPTER 1. INTRODUCTION 8 Solution.
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CHAPTER 1. INTRODUCTION 10 Let’s
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CHAPTER 1. INTRODUCTION 12 Out[8]:
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CHAPTER 1. INTRODUCTION 14 Press ]
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CHAPTER 1. INTRODUCTION 16 Matrix o
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CHAPTER 1. INTRODUCTION 18 stdlib/v
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CHAPTER 1. INTRODUCTION 20 In [37]:
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CHAPTER 1. INTRODUCTION 24 -0.62988
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CHAPTER 1. INTRODUCTION 26 5 7 9 He
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CHAPTER 1. INTRODUCTION 28 Sometime
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CHAPTER 1. INTRODUCTION 30 where s
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CHAPTER 1. INTRODUCTION 32 Notice t
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CHAPTER 1. INTRODUCTION 34 and real
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CHAPTER 1. INTRODUCTION 38 Chopping
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CHAPTER 1. INTRODUCTION 40 Machine
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CHAPTER 1. INTRODUCTION 42 The abso
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CHAPTER 1. INTRODUCTION 44 Next wil
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CHAPTER 1. INTRODUCTION 48 Exercise
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CHAPTER 1. INTRODUCTION 50 Sources
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CHAPTER 2. SOLUTIONS OF EQUATIONS:
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Chapter 3 Interpolation In this cha
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CHAPTER 3. INTERPOLATION 90 Here is
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CHAPTER 3. INTERPOLATION 92 basis f
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CHAPTER 3. INTERPOLATION 94 therefo
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CHAPTER 3. INTERPOLATION 96 Summary
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CHAPTER 3. INTERPOLATION 98 and thu
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CHAPTER 3. INTERPOLATION 100 With t
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CHAPTER 3. INTERPOLATION 102 Exampl
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CHAPTER 3. INTERPOLATION 104 Exerci
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CHAPTER 3. INTERPOLATION 106 end en
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CHAPTER 3. INTERPOLATION 108 increa
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CHAPTER 3. INTERPOLATION 110 The ne
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CHAPTER 3. INTERPOLATION 112 there
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CHAPTER 3. INTERPOLATION 114 Figure
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CHAPTER 3. INTERPOLATION 116 Then t
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CHAPTER 3. INTERPOLATION 120 Exerci
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CHAPTER 3. INTERPOLATION 122 yi yi+
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CHAPTER 3. INTERPOLATION 124 • Cl
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CHAPTER 3. INTERPOLATION 126 In [2]
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CHAPTER 3. INTERPOLATION 128 end fo
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CHAPTER 3. INTERPOLATION 132 end u=
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CHAPTER 3. INTERPOLATION 134 Especi
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CHAPTER 3. INTERPOLATION 136 Arya a
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CHAPTER 3. INTERPOLATION 138 This l
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CHAPTER 3. INTERPOLATION 140 Recrea
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CHAPTER 4. NUMERICAL QUADRATURE AND
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Page 221 and 222: Index Absolute error, 38 Beasley-Sp
Page 223 and 224: INDEX 220 Chebyshev, 203 Julia code
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First Semester in Numerical Analysis with Julia, 2020a

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