First Semester in Numerical Analysis with Julia, 2020a

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CHAPTER 1. INTRODUCTION 17 Out[23]: 3×3 Array{Float64,2}: -0.59693 0.227402 0.382604 0.0805382 -0.824332 0.154728 0.516392 0.59693 0.462668 In [24]: A*inv(A) Out[24]: 3×3 Array{Float64,2}: 1.0 -5.55112e-17 0.0 1.38778e-16 1.0 1.249e-16 -2.22045e-16 0.0 1.0 Let’s try matrix vector multiplication. Define some vector v as: In [25]: v=[0 0 1] Out[25]: 1×3 Array{Int64,2}: 0 0 1 Now try A ∗ v to multiply them. In [26]: A*v DimensionMismatch("matrix A has dimensions (3,3), matrix B has dimensions (1,3)") Stacktrace: [1] _generic_matmatmul!(::Array{Float64,2}, ::Char, ::Char, ::Array{Float64,2},::Array{Int64,2}) at /Users/osx/buildbot/slave/ package_osx64/build/usr/share/julia/stdlib/v1.1/LinearAlgebra/src/matmul.jl:591 [2] generic_matmatmul!(::Array{Float64,2}, ::Char, ::Char, ::Array{Float64,2}, ::Array{Int64,2}) at /Users/osx/buildbot/slave/ package_osx64/build/usr/share/julia/stdlib/v1.1/LinearAlgebra/src/matmul.jl:581 [3] mul! at /Users/osx/buildbot/slave/package_osx64/build/usr/share/julia/
CHAPTER 1. INTRODUCTION 18 stdlib/v1.1/LinearAlgebra/src/matmul.jl:175 [inlined] [4] *(::Array{Float64,2}, ::Array{Int64,2}) at /Users/osx/buildbot/slave/ package_osx64/build/usr/share/julia/stdlib/v1.1/LinearAlgebra/src/matmul.jl:142 [5] top-level scope at In[26]:1 What went wrong? The dimensions do not match. A is3by3,butv is1by3. To enter v asa3by1matrix, we need to type it as follows, using the transpose operation. (Check out the correct dimension displayed in the output.) In [27]: v=[0 0 1]' Out[27]: 3×1 LinearAlgebra.Adjoint{Int64,Array{Int64,2}}: 0 0 1 In [28]: A*v Out[28]: 3×1 Array{Float64,2}: 0.74 0.26 1.0 To solve the matrix equation Ax = v, type: In [29]: A\v Out[29]: 3×1 Array{Float64,2}: 0.3826037521318931 0.15472806518855411 0.4626681826795528 The solution to Ax = v can be also computed as x = A −1 v as follows: In [30]: inv(A)*v
Page 1 and 2: First Semester in Numerical Analysi
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Page 5 and 6: Contents 1 Introduction 5 1.1 Revie
Page 7 and 8: Preface This book is based on my le
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Page 11 and 12: CHAPTER 1. INTRODUCTION 8 Solution.
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Chapter 3 Interpolation In this cha
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CHAPTER 3. INTERPOLATION 96 Summary
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CHAPTER 3. INTERPOLATION 100 With t
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CHAPTER 3. INTERPOLATION 114 Figure
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CHAPTER 3. INTERPOLATION 120 Exerci
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CHAPTER 3. INTERPOLATION 126 In [2]
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CHAPTER 3. INTERPOLATION 140 Recrea
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CHAPTER 4. NUMERICAL QUADRATURE AND
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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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