MATLAB Mathematics - SERC - Index of

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Index LU factorization 6-30 minimum degree ordering 6-29 reducing bandwidth 6-29 representing mathematical functions 4-3 rigid body (ODE example) 5-19 rigidode demo 5-19 Robertson problem DAE example 5-35 ODE example 5-42 roots polynomial 2-3 S sampled data with ODE solvers 5-47 save 6-12 scalar as a matrix 1-5 scalar product 1-8 scattered data multidimensional interpolation 2-34 multidimensional tessellation 2-26 triangulation and interpolation 2-18 Schur decomposition 1-41 seamount data set 2-19 second difference operator example 6-9 shockbvp demo 5-73 singular value matrix decomposition 1-42 size sparse matrices 6-25 solution changes, rapid making initial guess 5-73 verifying consistent behavior 5-76 solving linear systems of equations full 1-13 sparse 6-36 sort 6-29 sparse function converting full to sparse 6-7 sparse matrix advantages 6-5 and complex values 6-6 Cholesky factorization 6-33 computational considerations 6-25 contents 6-13 conversion from full 6-7 creating 6-7 directly 6-8 from diagonal elements 6-10 density 6-7 distance between nodes 6-22 eigenvalues 6-39 fill-in 6-22 importing 6-12 linear systems of equations 6-36 LU factorization 6-30 and reordering 6-30 mathematical operations 6-25 nonzero elements 6-13 maximum number 6-9 specifying when creating matrix 6-8 storage 6-5, 6-13 values 6-13 nonzero elements of sparse matrix number of 6-13 operations 6-25 permutation 6-26 preconditioner 6-35 propagation through computations 6-25 QR factorization 6-34 Index-8
Index reordering 6-26 storage 6-5 for various permutations 6-28 viewing 6-13 triangular factorization 6-30 viewing contents graphically 6-15 viewing storage 6-13 visualizing 6-21 sparse ODE examples Brusselator system (brussode) 5-25 spconvert 6-12 spdiags 6-10 speye 6-26 spones 6-29 spparms 6-37 sprand 6-26 spy 6-15 spy plot 6-21 startup cost minimizing for ODE solvers 5-44 stiff ODE examples Brusselator system (brussode) 5-25 differential-algebraic problem (hb1dae) 5-35 finite element discretization (fem1ode) 5-22 van der Pol (vdpode) 5-20 stiffness (ODE), defined 5-12 storage minimizing for ODE problems 5-44 permutations of sparse matrices 6-28 sparse and full, comparison 6-6 sparse matrix 6-5 viewing for sparse matrix 6-13 sum counting nonzeros in sparse matrix 6-29 sparse matrices 6-26 sunspot periodicity calculating using Fourier transforms 3-3 symamd minimum degree ordering 6-30 symmetric matrix transpose 1-7 symrcm column permutation 6-31 reducing sparse matrix bandwidth 6-29 systems of equations. See linear systems of equations T tessellations, multidimensional Delaunay 2-29 Voronoi diagrams 2-31 theoretical graph 6-17 example 6-18 node 6-17 threebvp demo 5-63 three-dimensional interpolation 2-16 transfer functions using partial fraction expansion 2-7 transpose complex conjugate 1-8 unconjugated complex 1-8 triangular factorization sparse matrices 6-30 triangular matrix 1-27 triangulation closest point searches 2-24 Delaunay 2-20 scattered data 2-18 Voronoi diagrams 2-25 See also tessellation tricubic interpolation 2-16 trilinear interpolation 2-16 troubleshooting (ODE) 5-43 Index-9
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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 Vecto
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1 Matrices and Linear Algebra If A
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1 Matrices and Linear Algebra Inver
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1 Matrices and Linear Algebra X = p
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1 Matrices and Linear Algebra In co
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1 Matrices and Linear Algebra Matri
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1 Matrices and Linear Algebra compu
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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 Singu
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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 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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5 Differential Equations and the ri
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5 Differential Equations u1(x,t) 1
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5 Differential Equations Selected B
Page 242 and 243: 6 Sparse Matrices Function Summary
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Page 286 and 287: Index comparing sparse and full mat
Page 288 and 289: Index H hb1dae demo 5-35 hb1ode dem
Page 290 and 291: Index nonstiff ODE examples rigid b
Page 294: Index twobvp demo 5-63 two-dimensio
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