MATLAB Mathematics - SERC - Index of
MATLAB Mathematics - SERC - Index of MATLAB Mathematics - SERC - Index of
Index H hb1dae demo 5-35 hb1ode demo 5-42 Hermitian positive definite matrix 1-28 higher-order ODEs rewriting as first-order ODEs 5-5 I iburgersode demo 5-43 identity matrix 1-10 ihb1dae demo 5-42 importing sparse matrix 6-12 incomplete factorization 6-35 infeasible optimization problems 4-26 initial conditions ODE 5-4 ODE example 5-10 PDE 5-91 PDE example 5-96 initial guess (BVP) example 5-70 quality of 5-72 initial value problems DDE 5-49 defined 5-4 ODE and DAE 5-2 initial-boundary value PDE problems 5-89 inner product 1-7 integration double 4-28 numerical 4-27 triple 4-27 See also differential equations integration interval DDE 5-52 PDE (MATLAB) 5-93 interpolation 2-9 comparing methods graphically 2-13 FFT-based 2-12 multidimensional 2-16 scattered data 2-34 one-dimensional 2-10 speed, memory, smoothness 2-11 three-dimensional 2-16 two-dimensional 2-12 inverse of matrix 1-22 iterative methods sparse matrices 6-37 sparse systems of equations 6-36 K Kronecker tensor matrix product 1-11 L least squares 6-34 length of curve, computing 4-27 linear algebra 1-4 linear equations minimal norm solution 1-25 overdetermined systems 1-18 rectangular systems 1-23 underdetermined systems 1-20 linear interpolation multidimensional 2-17 one-dimensional 2-10 linear systems of equations direct methods (sparse) 6-36 full 1-13 iterative methods (sparse) 6-36 sparse 6-36 Index-4
Index linear transformation 1-4 load sparse matrices 6-12 Lobatto IIIa BVP solver 5-65 LU factorization 1-29 sparse matrices and reordering 6-30 M mat4bvp demo 5-63 mat4bvp demo 5-68 mathematical functions as function input arguments 4-1 finding zeros 4-21 minimizing 4-8 numerical integration 4-27 plotting 4-5 representing in MATLAB 4-3 mathematical operations sparse matrices 6-25 Mathieu’s equation (BVP example) 5-68 matrices 1-4 as linear transformation 1-4 characteristic polynomial 2-4 characteristic roots 2-4 creation 1-4 determinant 1-22 full to sparse conversion 6-7 identity 1-10 inverse 1-22 iterative methods (sparse) 6-37 orthogonal 1-30 pseudoinverse 1-23 rank deficiency 1-20 symmetric 1-7 triangular 1-27 matrix operations addition and subtraction 1-6 division 1-13 exponentials 1-35 multiplication 1-8 powers 1-34 transpose 1-7 matrix products Kronecker tensor 1-11 max 6-26 M-files representing mathematical functions 4-3 minimizing mathematical functions of one variable 4-8 of several variables 4-9 options 4-13 minimum degree ordering 6-29 Moore-Penrose pseudoinverse 1-23 multidimensional data gridding 2-17 interpolation 2-16 multidimensional interpolation 2-16 scattered data 2-26 multistep solver (ODE) 5-6 N nearest neighbor interpolation multidimensional 2-17 one-dimensional 2-10 three-dimensional 2-16 two-dimensional 2-12 nnz 6-13 nodes 6-17 distance between 6-22 numbering 6-19 Index-5
- Page 238 and 239: 5 Differential Equations u1(x,t) 1
- Page 240 and 241: 5 Differential Equations Selected B
- Page 242 and 243: 6 Sparse Matrices Function Summary
- Page 244 and 245: 6 Sparse Matrices Function Summary
- Page 246 and 247: 6 Sparse Matrices This matrix requi
- Page 248 and 249: 6 Sparse Matrices S = (3,1) 1 (2,2)
- Page 250 and 251: 6 Sparse Matrices Now F = full(S) d
- Page 252 and 253: 6 Sparse Matrices Importing Sparse
- Page 254 and 255: 6 Sparse Matrices west0479 west0479
- Page 256 and 257: 6 Sparse Matrices The find Function
- Page 258 and 259: 6 Sparse Matrices of the rows and c
- Page 260 and 261: 6 Sparse Matrices The vertices of o
- Page 262 and 263: 6 Sparse Matrices 0 10 20 30 40 50
- Page 264 and 265: 6 Sparse Matrices 0 500 1000 1500 2
- Page 266 and 267: 6 Sparse Matrices simply sparse(m,n
- Page 268 and 269: 6 Sparse Matrices Similarly, S(:,p)
- Page 270 and 271: 6 Sparse Matrices The following MAT
- Page 272 and 273: 6 Sparse Matrices 0 Original 0 Reve
- Page 274 and 275: 6 Sparse Matrices QR Factorization
- Page 276 and 277: 6 Sparse Matrices shows that A has
- Page 278 and 279: 6 Sparse Matrices Functions for Ite
- Page 280 and 281: 6 Sparse Matrices set up the five-p
- Page 282 and 283: 6 Sparse Matrices Manipulating Spar
- Page 284 and 285: 6 Sparse Matrices Selected Bibliogr
- Page 286 and 287: Index comparing sparse and full mat
- Page 290 and 291: Index nonstiff ODE examples rigid b
- Page 292 and 293: Index LU factorization 6-30 minimum
- Page 294: Index twobvp demo 5-63 two-dimensio
<strong>Index</strong><br />
linear transformation 1-4<br />
load<br />
sparse matrices 6-12<br />
Lobatto IIIa BVP solver 5-65<br />
LU factorization 1-29<br />
sparse matrices and reordering 6-30<br />
M<br />
mat4bvp demo 5-63<br />
mat4bvp demo 5-68<br />
mathematical functions<br />
as function input arguments 4-1<br />
finding zeros 4-21<br />
minimizing 4-8<br />
numerical integration 4-27<br />
plotting 4-5<br />
representing in <strong>MATLAB</strong> 4-3<br />
mathematical operations<br />
sparse matrices 6-25<br />
Mathieu’s equation (BVP example) 5-68<br />
matrices 1-4<br />
as linear transformation 1-4<br />
characteristic polynomial 2-4<br />
characteristic roots 2-4<br />
creation 1-4<br />
determinant 1-22<br />
full to sparse conversion 6-7<br />
identity 1-10<br />
inverse 1-22<br />
iterative methods (sparse) 6-37<br />
orthogonal 1-30<br />
pseudoinverse 1-23<br />
rank deficiency 1-20<br />
symmetric 1-7<br />
triangular 1-27<br />
matrix operations<br />
addition and subtraction 1-6<br />
division 1-13<br />
exponentials 1-35<br />
multiplication 1-8<br />
powers 1-34<br />
transpose 1-7<br />
matrix products<br />
Kronecker tensor 1-11<br />
max 6-26<br />
M-files<br />
representing mathematical functions 4-3<br />
minimizing mathematical functions<br />
<strong>of</strong> one variable 4-8<br />
<strong>of</strong> several variables 4-9<br />
options 4-13<br />
minimum degree ordering 6-29<br />
Moore-Penrose pseudoinverse 1-23<br />
multidimensional<br />
data gridding 2-17<br />
interpolation 2-16<br />
multidimensional interpolation 2-16<br />
scattered data 2-26<br />
multistep solver (ODE) 5-6<br />
N<br />
nearest neighbor interpolation<br />
multidimensional 2-17<br />
one-dimensional 2-10<br />
three-dimensional 2-16<br />
two-dimensional 2-12<br />
nnz 6-13<br />
nodes 6-17<br />
distance between 6-22<br />
numbering 6-19<br />
<strong>Index</strong>-5
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