First Semester in Numerical Analysis with Julia, 2020a

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CHAPTER 3. INTERPOLATION 129 end m=length(x) if wx[m] return print("error: spline evaluated outside its domain") end n=m-1 p=1 for i in 1:n if w
CHAPTER 3. INTERPOLATION 130 end end return(a) Out[4]: diff (generic function with 1 method) In [5]: function newton(x::Array,y::Array,z) m=length(x) # here m is the number of data points, not the # degree of the polynomial a=diff(x,y) sum=a[1] pr=1.0 for j in 1:(m-1) pr=pr*(z-x[j]) sum=sum+a[j+1]*pr end return sum end Out[5]: newton (generic function with 1 method) Here is the code that computes the cubic spline, Newton interpolation, and plot them. In [6]: using LaTeXStrings xaxis=-5:1/100:5 f(x)=1/(1+x^2) runge=f.(xaxis) xi=collect(-5:1:5) yi=map(f,xi) CubicNatural(xi,yi) naturalspline=map(z->CubicNaturalEval(z,xi),xaxis) interp=map(z->newton(xi,yi,z),xaxis) # Interpolating polynomial # for the data plot(xaxis,runge,label=L"1/(1+x^2)") plot(xaxis,interp,label="Interpolating poly") plot(xaxis,naturalspline,label="Natural cubic spline")
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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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Page 181 and 182: Chapter 5 Approximation Theory 5.1
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CHAPTER 5. APPROXIMATION THEORY 180
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Index Absolute error, 38 Beasley-Sp
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INDEX 220 Chebyshev, 203 Julia code
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First Semester in Numerical Analysis with Julia, 2020a

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