First Semester in Numerical Analysis with Julia, 2020a

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References [1] Abramowitz, M., and Stegun, I.A., 1965. Handbook of mathematical functions: with formulas, graphs, and mathematical tables (Vol. 55). Courier Corporation. [2] Chace, A.B., and Manning, H.P., 1927. The Rhind Mathematical Papyrus: British Museum 10057 and 10058. Vol 1. Mathematical Association of America. [3] Atkinson, K.E., 1989. An Introduction to Numerical Analysis, Second Edition, John Wiley & Sons. [4] Burden, R.L, Faires, D., and Burden, A.M., 2016. Numerical Analysis, 10th Edition, Cengage. [5] Capstick, S., and Keister, B.D., 1996. Multidimensional quadrature algorithms at higher degree and/or dimension. Journal of Computational Physics, 123(2), pp.267-273. [6] Chan, T.F., Golub, G.H., and LeVeque, R.J., 1983. Algorithms for computing the sample variance: Analysis and recommendations. The American Statistician, 37(3), pp.242-247. [7] Cheney, E.W., and Kincaid, D.R., 2012. Numerical mathematics and computing. Cengage Learning. [8] Glasserman, P., 2013. Monte Carlo methods in Financial Engineering. Springer. [9] Goldberg, D., 1991. What every computer scientist should know about floating-point arithmetic. ACM Computing Surveys (CSUR), 23(1), pp.5-48. [10] Heath, M.T., 1997. Scientific Computing: An introductory survey. McGraw-Hill. [11] Higham, N.J., 1993. The accuracy of floating point summation. SIAM Journal on Scientific Computing, 14(4), pp.783-799. [12] Isaacson, E., and Keller, H.B., 1966. Analysis of Numerical Methods. John Wiley & Sons. 217
Index Absolute error, 38 Beasley-Springer-Moro, 165 Biased exponent, 31 Big O notation, 91 Bisection method, 55 error theorem, 58 Julia code, 56 linear convergence, 58 Black-Scholes-Merton formula, 65 Chebyshev nodes, 111 Chebyshev polynomials, 203 Julia code, 211 Chopping, 38 Composite Newton-Cotes, 147 midpoint, 148 roundoff, 152 Simpson, 148 trapezoidal, 148 Degree of accuracy, 144 Divided differences, 98 derivative formula, 112 Dr. Seuss, 136 Extreme value theorem, 7 Fixed-point iteration, 76, 78 application to Newton’s method, 86 error theorem, 81 geometric interpretation, 78 high-order, 85 high-order error theorem, 86 Julia code, 80 Floating-point, 29 decimal, 37 IEEE 64-bit, 30 infinity, 32 NAN, 32 normalized, 30 toy model, 33 zero, 32 Gamma function, 101 Gaussian quadrature, 152 error theorem, 158 Julia code, 157 Legendre polynomials, 154 Gram-Schmidt process, 202 Hermite interpolation, 112 computation, 115 Julia code, 117 Implied volatility, 66 Improper integrals, 167 Intermediate value theorem, 7 Interpolation, 88 Inverse interpolation, 107 Iterative method, 53 218
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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 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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