MATLAB Mathematics - SERC - Index of

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Index comparing sparse and full matrix storage 6-6 complex values in sparse matrix 6-6 computational functions applying to sparse matrices 6-25 computational geometry multidimensional 2-26 two-dimensional 2-18 contents of sparse matrix 6-13 convex hulls multidimensional 2-27 two-dimensional 2-20 convolution 2-5 creating sparse matrix 6-8 cubic interpolation multidimensional 2-17 one-dimensional 2-11 spline 2-11 curve fitting polynomial 2-6 curves computing length 4-27 Cuthill-McKee reverse ordering 6-29 D DAE solution of 5-2 data gridding multidimensional 2-17 DDE 5-49 rewriting as first-order system 5-54 DDE solver 5-51 basic syntax 5-52 discontinuities 5-57 evaluating solution at specific points 5-56 examples cardiovascular model (ddex2) 5-58 straightforward example (ddex1) 5-53 performance 5-60 representing problems 5-53 ddex1 demo 5-53 ddex2 demo 5-58 decomposition eigenvalue 1-38 Schur 1-41 singular value 1-42 deconvolution 2-5 Delaunay tessellations 2-29 Delaunay triangulation 2-20 closest point searches 2-24 Delay Differential Equations. See DDE density sparse matrix 6-7 derivatives polynomial 2-5 determinant of matrix 1-22 diag 6-26 diagonal creating sparse matrix from 6-10 differential equations 5-1 boundary value problems for ODEs 5-61 initial value problems for DAEs 5-2 initial value problems for DDEs 5-49 initial value problems for ODEs 5-2 partial differential equations 5-89 differential-algebraic equations. See DAE direct methods systems of sparse equations 6-36 discontinuities DDE solver 5-57 Index-2
Index displaying sparse matrices 6-15 distance between nodes 6-22 dot product 1-8 E eigenvalues 1-38 of sparse matrix 6-39 eigenvectors 1-38 electrical circuits DAE example 5-42 Emden’s equation example 5-81 error tolerance effects of too large (ODE) 5-47 machine precision 5-45 event location (ODE) advanced example 5-32 simple example 5-28 eye derivation of the name 1-10 sparse matrices 6-25 triangular 6-30 fem1ode demo 5-22 fem2ode demo 5-42 fill-in of sparse matrix 6-22 find function sparse matrices 6-16 finite element discretization (ODE example) 5-22 first-order differential equations representation for BVP solver 5-69 representation for DDE solver 5-54 Fourier analysis concepts 3-2 Fourier transforms calculating sunspot periodicity 3-3 FFT-based interpolation 2-12 length vs. speed 3-9 phase and magnitude of transformed data 3-7 fsbvp demo 5-76 full 6-26, 6-29 function functions 4-1 functions mathematical. See mathematical functions optimizing 4-8 F factorization 6-30 Cholesky 1-27 Hermitian positive definite 1-28 incomplete 6-35 LU 1-29 partial pivoting 1-29 positive definite 1-27 QR 1-30 sparse matrices 6-30 Cholesky 6-33 LU 6-30 G Gaussian elimination 1-29 geodesic dome 6-18 geometric analysis multidimensional 2-26 two-dimensional 2-18 global minimum 4-26 global variables 4-30 gplot 6-18 graph characteristics 6-21 defined 6-17 Index-3
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MATLAB® The Language of Technical
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Revision History June 2004 First pr
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2 Polynomials and Interpolation Pol
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Introduction to Initial Value ODE P
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vi Contents
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1 Matrices and Linear Algebra Funct
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1 Matrices and Linear Algebra Matri
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1 Matrices and Linear Algebra Addin
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1 Matrices and Linear Algebra If x
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1 Matrices and Linear Algebra y = v
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1 Matrices and Linear Algebra Inver
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1 Matrices and Linear Algebra Eigen
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1 Matrices and Linear Algebra produ
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1 Matrices and Linear Algebra 1-44
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2 Polynomials and Interpolation Pol
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2 Polynomials and Interpolation pol
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2 Polynomials and Interpolation Cal
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2 Polynomials and Interpolation whe
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2 Polynomials and Interpolation Int
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2 Polynomials and Interpolation 2 G
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2 Polynomials and Interpolation for
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2 Polynomials and Interpolation Con
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2 Polynomials and Interpolation Lat
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2 Polynomials and Interpolation −
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2 Polynomials and Interpolation −
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2 Polynomials and Interpolation 7 3
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2 Polynomials and Interpolation T =
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2 Polynomials and Interpolation Bec
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2 Polynomials and Interpolation 2-3
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2 Polynomials and Interpolation 2-3
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3 Fast Fourier Transform (FFT) Intr
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3 Fast Fourier Transform (FFT) 200
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3 Fast Fourier Transform (FFT) 2 x
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3 Fast Fourier Transform (FFT) 500
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3 Fast Fourier Transform (FFT) Func
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4 Function Functions Function Summa
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4 Function Functions You can also c
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4 Function Functions 25 20 15 10 5
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4 Function Functions Minimizing Fun
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4 Function Functions To try fminsea
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4 Function Functions Plotting the R
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4 Function Functions The number of
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4 Function Functions and displays t
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4 Function Functions end function s
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4 Function Functions States of the
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4 Function Functions 100 80 60 40 2
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4 Function Functions You can verify
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4 Function Functions Troubleshootin
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4 Function Functions A three-dimens
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4 Function Functions Parameterizing
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4 Function Functions “Anonymous F
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5 Differential Equations Initial Va
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5 Differential Equations odephas3 o
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5 Differential Equations This secti
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5 Differential Equations The basic
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5 Differential Equations 2 Code the
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5 Differential Equations function.
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5 Differential Equations One way to
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5 Differential Equations y0, yp0 Ve
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5 Differential Equations For exampl
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5 Differential Equations 1 0.8 0.6
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5 Differential Equations 2.5 Soluti
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5 Differential Equations To run thi
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5 Differential Equations 2 u′ i =
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5 Differential Equations dydt(i+1,:
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5 Differential Equations refine = 4
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5 Differential Equations Example: A
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5 Differential Equations function [
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5 Differential Equations Note The R
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5 Differential Equations 1 Robertso
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5 Differential Equations The MATLAB
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5 Differential Equations Summary of
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5 Differential Equations Problem Si
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5 Differential Equations Error Tole
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5 Differential Equations Troublesho
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5 Differential Equations Function d
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5 Differential Equations dde23 prod
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5 Differential Equations The exampl
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5 Differential Equations solution y
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5 Differential Equations Example: C
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5 Differential Equations Changing D
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5 Differential Equations BVP Functi
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5 Differential Equations two-point
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5 Differential Equations The input
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5 Differential Equations 2 Pass the
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5 Differential Equations Finding Un
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5 Differential Equations vectorized
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5 Differential Equations There is a
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5 Differential Equations 3 Solve on
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5 Differential Equations hold off T
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5 Differential Equations Note The d
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5 Differential Equations legend('An
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5 Differential Equations Here, v(1-
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5 Differential Equations solution v
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5 Differential Equations Note The D
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5 Differential Equations After disc
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5 Differential Equations The output
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5 Differential Equations Note See t
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5 Differential Equations The exampl
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