absolute accuracy
BVP
DDE
ODE
additional parameters
BVP example <1> <2>
ODE example
adjacency matrix
and graphing
Bucky ball
defined
distance between nodes
node
numbering nodes
airflow modeling
amp1dae demo
analytical partial derivatives (BVP)
ballode demo
bandwidth of sparse matrix, reducing
Basic Fitting interface
batonode demo
bicubic interpolation
bilinear interpolation
boundary conditions
BVP
BVP example
PDE
PDE example
Boundary Value Problems. See BVP
Brusselator system (ODE example)
brussode demo
Buckminster Fuller dome
Bucky ball
burgersode demo
BVP
defined
rewriting problem as first-order system
BVP solver
additional known parameters
basic syntax
evaluate solution at specific points
examples
boundary condition at infinity (shockbvp)
Mathieu's Equation (mat4bvp)
rapid solution changes (shockbvp)
initial guess
performance
representing problems
unknown parameters
BVP solver properties
analytical partial derivatives
bvpset function
error tolerance
Jacobian matrix
mesh
modifying property structure
querying property structure
singular BVPs
solution statistics
vectorization
cat
characteristic polynomial of matrix
characteristic roots of matrix
chol <1> <2>
Cholesky factorization
for sparse matrices
closest point searches
Delaunay triangulation
colamd
colmmd <1> <2>
colperm
comparing
sparse and full matrix storage
complex values in sparse matrix
computational functions
applying to sparse matrices
computational geometry
multidimensional
two-dimensional
condest
contents of sparse matrix
convex hulls
multidimensional
two-dimensional
convolution
correlation coefficients
covariance
creating
sparse matrix
cubic interpolation
multidimensional
one-dimensional
cubic spline interpolation
curve fitting
Basic Fitting interface
error bounds
exponential
polynomial <1> <2>
curves
computing length
Cuthill-McKee, reverse ordering
DAE
solution of
data analysis
column-oriented
data filtering. See filtering
data fitting. See curve fittimg
data gridding
multidimensional
data. See also
multivariate data
statistical data
univariate data
DDE
rewriting problem as first-order system
DDE solver
additional known parameters
basic syntax
discontinuities
evaluating solution at specific points
examples
cardiovascular model (ddex2)
straightforward example (ddex1)
performance
representing problems
DDE solver properties
ddeset function
error tolerance
event location
modifying property structure
querying property structure
solver output
step size
ddephas2 output function
ddephas3 output function
ddeplot output function
ddeprint output function
ddex1 demo
ddex2 demo
decomposition
eigenvalue
Schur
singular value
deconvolution
Delaunay multidimensional tessellations
Delaunay triangulation
closest point searches
Delay Differential Equations. See DDE
density of sparse matrix
derivatives
polynomial
determinant of matrix
diag
diagonal
creating sparse matrix from
difference equations
differential equations
boundary value problems for ODEs
initial value problems for DDEs
initial value problems for ODEs and DAEs
partial differential equations
differential-algebraic equations. See DAE
direct methods for systems of equations
discontinuities (DDE)
discrete Fourier transform. See Fourier transforms
displaying
sparse matrices
distance between nodes
dot product
eigenvalues
of sparse matrix
eigenvectors
Emden's equation
example
error bounds
curve fitting
error tolerance
BVP problems
DDE problems
effects of too large (ODE)
machine precision
ODE problems
event location (DDE)
event location (ODE)
advanced example
simple example
examples
adjacency matrix (sparse)
airflow modeling
Bucky ball
second difference operator
sparse matrix <1> <2>
theoretical graph (sparse)
examples (BVP)
boundary condition at infinity (fsbvp)
Mathieu's Equation (mat4bvp)
rapid solution changes (shockbvp)
two solutions (twobvp)
examples (DAE)
electrical circuit (amp1dae)
Robertson problem (hb1dae)
examples (DDE)
cardiovascular model (ddex2)
straightforward example (ddex1)
examples (MATLAB PDE)
electrodynamics problem (pdex4)
simple PDE (pdex1)
examples (ODE)
advanced event location (orbitode)
Brusselator system (brussode)
constant mass matrix (fem2ode)
finite element discretization (fem1ode)
nonstiff
rigid body (rigidode)
Robertson problem (hb1ode)
simple event location (ballode)
stiff
strongly state-dependent mass matrix (burgersode)
time-, state-dependent mass matrix (batonode)
van der Pol (vdpode)
exponential curve fitting
eye
derivation of the name
factorization
Cholesky
for sparse matrices
Cholesky
LU
triangular
Hermitian positive definite
incomplete
LU
partial pivoting
positive definite
QR
fast Fourier transform. See Fourier transforms
fem1ode demo
fem2ode demo
fill-in of sparse matrix
filtering
difference equations
find function
and sparse matrices
finite differences
finite element discretization (ODE example)
first-order differential equations
representation for BVP solver
representation for DDE solver
Fourier analysis
concepts
Fourier transforms
calculating sunspot periodicity
FFT-based interpolation
length vs. speed
phase and magnitude of transformed data
fsbvp demo
full <1> <2>
function functions
functions
mathematical. See mathematical functions
optimizing
Gaussian elimination
geodesic dome
geometric analysis
multidimensional
two-dimensional
global minimum
gplot
graph
characteristics
defined
theoretical
hb1dae demo
hb1ode demo
Hermitian positive definite matrix
higher-order ODEs
rewriting as system of first-order ODEs
identity matrix
importing
sparse matrix
incomplete factorization
infeasible optimization problems
initial conditions
ODE
ODE example
PDE
PDE example
initial guess (BVP)
example
quality of
initial value problems
DDE
defined
ODE and DAE
initial-boundary value PDE problems
inline objects
representing mathematical functions
inner product
integration
double
numerical
See also differential equations
integration interval
DDE
ODE
PDE (MATLAB)
interpolation
comparing methods graphically
FFT-based
multidimensional
scattered data
one-dimensional
speed, memory, smoothness
three-dimensional
two-dimensional
inverse of matrix
iterative methods
for sparse matrices
for systems of equations
Jacobian matrix (BVP)
Jacobian matrix (ODE)
generating sparse numerically
specifying
vectorizing ODE function
Kronecker tensor matrix product
least squares
length of curve, computing
linear algebra
linear equations
minimal norm solution
overdetermined systems
rectangular systems
underdetermined systems
linear interpolation
multidimensional
one-dimensional
linear systems of equations
direct methods
full
iterative methods
sparse
linear transformation
load
Lobatto IIIa BVP solver
lu <1> <2>
LU factorization
for sparse matrices and reordering
mass matrix (ODE)
initial slope
singular
sparsity pattern
specifying
state dependence
mat4bvp demo
mat4bvp demo
mathematical functions
as function input arguments
finding zeros
minimizing
numerical integration
plotting
representing in MATLAB
mathematical operations on sparse matrices
Mathieu's equation (BVP example)
matrices
as linear transformation
characteristic polynomial
characteristic roots
creation
determinant
full to sparse conversion <1> <2>
identity
inverse
orthogonal
pseudoinverse
rank deficiency
symmetric
triangular
matrix
iterative methods
matrix operations
addition and subtraction
division
exponentials
multiplication
powers
transpose
matrix products
Kronecker tensor
max
mesh size (BVP)
M-files
representing mathematical functions
minimizing mathematical functions
of one variable
of several variables
options
minimum degree ordering
Moore-Penrose pseudoinverse
multidimensional data gridding
multidimensional interpolation
scattered data
multistep solver (ODE)
multivariate data
matrix representation
vehicle traffic sample data
NaNs
propagation
removing from data
nearest neighbor interpolation
multidimensional
one-dimensional
three-dimensional
two-dimensional
nnz <1> <2>
nodes
distance between
numbering
nonstiff ODE examples
rigid body (rigidode)
nonzero elements
number of
nonzero elements of sparse matrix
maximum number in sparse matrix
storage <1> <2>
values
visualizing with spy plot
nonzeros
normalizing data
norms
vector and matrix
numerical integration
computing length of curve
double
nzmax <1> <2>
objective function
return values
ODE
coding in MATLAB
defined
overspecified systems
solution of
ODE solver
evaluate solution at specific points
ODE solver properties
error tolerance
event location
fixed step sizes
Jacobian matrix
mass matrix
modifying property structure
ode15s
odeset function
querying property structure
solver output
step size
ODE solvers
algorithms
Adams-Bashworth-Moulton PECE
Bogacki-Shampine
Dormand-Prince
modified Rosenbrock formula
numerical differentiation formulas
backward differentiation formulas
backwards in time
basic example
stiff problem
basic syntax
calling
examples
minimizing output storage
minimizing startup cost
multistep solver
nonstiff problem example
nonstiff problems
numerical differentiation formulas
obtaining solutions at specific times
one-step solver
overview
passing additional parameters
performance
problem size
representing problems
sampled data
stiff problems <1> <2>
troubleshooting
variable order solver
odephas2 output function
odephas3 output function
odeplot output function
odeprint output function
one-dimensional interpolation
ones
one-step solver (ODE)
operator
second difference
optimization
calling sequence changes (Version 5)
helpful hints
options parameters
troubleshooting
See also minimizing mathematical functions
optimization code
updating to MATLAB Version 5 syntax
orbitode demo
Ordinary Differential Equations. See ODE
orthogonal matrix
outer product
outliers
removing from statistical data
output points (ODE)
increasing number of
output properties (DDE)
output properties (ODE)
increasing number of output points
output storage
minimizing for ODE problems
overdetermined
rectangular matrices
overspecified ODE systems
Partial Differential Equations. See PDE
partial fraction expansion
PDE
defined
discretized
PDE solver (MATLAB)
additional known parameters
basic syntax
evaluate solution at specific points
examples
electrodynamics problem
simple PDE
performance
representing problems
PDE solver (MATLAB) properties
pdex1 demo
pdex2 demo
pdex3 demo
pdex4 demo
pdex5 demo
performance
de-emphasizing an ODE solution component
improving for BVP solver
improving for DDE solver
improving for ODE solvers
improving for PDE solver
permutations
plotting
mathematical functions
polynomial
curve fitting
regression
polynomial interpolation
polynomials
basic operations
calculating coefficients from roots
calculating roots
curve fitting
derivatives
evaluating
multiplying and dividing
partial fraction expansion
representing as vectors
preconditioner for sparse matrix
property structure (BVP)
creating
modifying
querying
property structure (DDE)
creating
modifying
querying
property structure (ODE)
creating
modifying
querying
pseudoinverse
of matrix
QR factorization <1> <2>
quad, quadl functions
differ from ODE solvers
quadrature. See numerical integration
rand
rank
deficiency
rank deficiency
detecting
rectangular matrices
rectangular matrices
identity
overdetermined systems
pseudoinverse
QR factorization
rank deficient
singular value decomposition
underdetermined systems
regression
linear-in-the-parameters
multiple
polynomial
relative accuracy
BVP
DDE
norm of DDE solution
norm of ODE solution
ODE
reorderings
and LU factorization
for sparser factorizations
minimum degree ordering
to reduce bandwidth
representing
mathematical functions
residuals
analyzing
for exponential data fit
rigid body (ODE example)
rigidode demo
Robertson problem
DAE example
ODE example
roots
polynomial
sampled data
with ODE solvers
save
scalar
as a matrix
scalar product
scattered data
multidimensional interpolation
multidimensional tessellation
triangulation and interpolation
Schur decomposition
seamount data set
second difference operator, example
shockbvp demo
singular value matrix decomposition
size
solution changes, rapid (BVP example) <1> <2>
solution statistics (BVP)
solving linear systems of equations
full
sparse
sort
sparse <1> <2>
sparse matrix
advantages
and complex values
Cholesky factorization
computational considerations
contents
conversion from full <1> <2>
creating
directly
from diagonal elements
defined
density
distance between nodes
eigenvalues
elementary
example
fill-in
importing
linear algebra
linear equations
linear systems of equations
LU factorization
and reordering
mathematical operations
nonzero elements
maximum number
specifying when creating matrix
storage <1> <2>
values
nonzero elements of sparse matrix
number of
operations
permutation
preconditioner
propagation through computations
QR factorization
reordering <1> <2>
storage
for various permutations
viewing
theoretical graph
triangular factorization
viewing contents graphically
viewing storage
visualizing
working with
sparse ODE examples
Brusselator system (brussode)
spconvert
spdiags
speye <1> <2> <3>
spones
spparms
sprand
spy
spy plot
startup cost
minimizing for ODE solvers
statistical data
missing values
normalizing
outliers
preprocessing
removing NaNs
See also multivariate data
See also univariate data
statistics
descriptive
step size (DDE)
initial step size
upper bound
step size (ODE) <1> <2>
initial step size
upper bound
stiff ODE examples
Brusselator system (brussode)
differential-algebraic problem (hb1dae)
finite element dicretization (fem1ode)
van der Pol (vdpode)
stiffness (ODE), defined
storage
for various permutations of sparse matrix
of sparse matrix
sparse and full, comparison
viewing for sparse matrix
sum <1> <2>
sunspot periodicity
calculating using Fourier transforms
symamd
symmetric
matrix
symmmd <1> <2>
symrcm <1> <2>
systems of equations. See linear systems of equations
tessellations, multidimensional
Delaunay
Voronoi diagrams
theoretical graph
example
node
three-dimensional interpolation
transfer functions
using partial fraction expansion
transpose
complex conjugate
unconjugated complex
triangular factorization
for sparse matrices
triangular matrix
triangulation
closest point searches
Delaunay
scattered data
Voronoi diagrams
See also tessellation
tricubic interpolation
trilinear interpolation
troubleshooting (ODE)
twobvp demo
two-dimensional interpolation
comparing methods graphically
underdetermined
rectangular matrices
unitary matrices
QR factorization
univariate data
unknown parameters (BVP)
example
updating optimization code to MATLAB Version 5 syntax
van der Pol example
simple, nonstiff
simple, stiff
variable-order solver (ODE)
vdpode demo
vector products
dot or scalar
outer and inner
vectorizing ODE function (BVP)
vectors
column and row
multiplication
vehicle traffic sample data
visualizing
sparse matrix
spy plot
visualizing solver results
BVP
DDE
ODE
PDE
Voronoi diagrams
multidimensional
two-dimensional
whos
zeros
of mathematical functions
zeros