abs
absolute accuracy
BVP
ODE
addition
of matrices
adjacency matrix
and graphing
Bucky ball
defined
distance between nodes
node
numbering nodes
airflow modeling
algorithms
ODE solvers
Adams-Bashworth-Moulton PECE
Bogacki-Shampine (2,3)
Dormand-Prince (4,5)
modified Rosenbrock formula
numerical differentiation formulas
amp1dae
analytical partial derivatives (BVP)
angle
arguments
for ODE file
arrays
elements
assignment statements
A-stable differentiation formulas
ballode <1> <2>
bandwidth of sparse matrix, reducing
Basic Fitting interface
batonode
bicubic interpolation <1> <2>
bilinear interpolation <1> <2>
boundary condition, ODE
Boundary Value Problems
defined
determining unknown parameters
passing additional known parameters <1> <2>
Boundary Value Problems, solver properties
analytical partial derivatives <1> <2>
BCJacobian
FJacobian
bvpset function
error tolerance <1> <2>
absolute accuracy
AbsTol
relative accuracy
RelTol
mesh <1> <2>
modifying property structure
querying property structure
solver output
Stats
Brusselator system (ODE example)
brussode <1> <2>
Buckminster Fuller dome
Bucky ball
burgersode
BVP. See Boundary Value Problems
bvpget
bvpset
calling MATLAB functions
ODE solvers
cat
characteristic polynomial
characteristic roots of matrix
chol <1> <2>
Cholesky factorization
for sparse matrices
closest point searches
colamd
colmmd <1> <2>
colon operator
colperm
column vector
for polynomial roots representation
of event locations (ODE)
comparing
interpolation methods
sparse and full matrix storage
complex conjugate transpose
complex values in sparse matrix
computational functions
applying to sparse matrices
condest
condition, dimension compatibility
conditions for ODEs
boundary
initial
confidence intervals
contents of sparse matrix
continuous extension (ODE solvers) <1> <2>
contour
contour plots, to compare interpolation methods
conv
convex hull
multidimensional
convhull
convhulln
convolution
corrcoef
correlation coefficients
cov
covariance
creating
sparse matrix
cubic interpolation
multidimensional
one-dimensional
cubic spline interpolation
curve fitting
confidence intervals
using the Basic Fitting interface
Cuthill-McKee, reverse ordering
data
filter
monotonic
multivariate
preprocessing
sorting
data analysis
finite differences
triangulation
data fitting
confidence intervals
error bounds
exponential fit
exponential fits
polynomial fits
using the Basic Fitting interface
data gridding
multidimensional
data normalization
decomposition
eigenvalue
Schur
singular value
deconv
deconvolution
Delaunay tesselations
Delaunay triangulation
closest point searches
delaunayn
density of sparse matrix
derivative of polynomial
descriptive statistics
det
determinant
diag
diagonal
creating sparse matrix from
of a matrix
diff
difference between successive vector elements
difference equations
differential equations
boundary value problems for ODEs
initial value problems for ODEs and DAEs
partial differential equations
dimension compatibility
direct methods for systems of equations
directories
funfun
discrete Fourier transform
displaying
sparse matrices
distance between nodes
division
matrix
of polynomials
dot product
dsearch
eig
eigenvalue
decomposition
eigenvalues
of sparse matrix
eigenvector
error
bound, for data fit
tolerance
boundary value problems
BVP
ODE <1> <2>
evaluating
polynomials in matrix sense
event location (ODE) <1> <2>
examples
adjacency matrix (sparse)
airflow modeling
brussode
Bucky ball
Delaunay triangulation
fem1ode
interpolation
ODE solvers
orbitode
rigidode
second difference operator
sparse matrix <1> <2>
theoretical graph (sparse)
van der Pol
extra parameters
stiff
vdpode
exponential fit to data
exponentials, matrix
eye <1> <2>
factorization
Cholesky
for sparse matrices
Cholesky
LU
triangular
Hermitian positive definite
incomplete
LU
positive definite
QR
fast Fourier transform. See Fourier transform, fast
fem1ode <1> <2>
fem1ode example
fem2ode
fft <1> <2>
FFT. See Fourier transform, fast
fill-in of sparse matrix
filtering
find function
and sparse matrices
finding
nonzero elements
finite differences
finite element discretization (ODE example)
first-order differential equations, representation for ODE solvers
fit. See data fitting
fminbnd <1> <2>
fminsearch
Fourier analysis
Fourier transform
fast
FFT-based interpolation
specifying length
fplot
full <1> <2>
function
minimizing
function functions <1> <2>
functions
optimization
funfun directory
fzero
Gaussian elimination <1> <2>
geodesic dome
gplot
graph
characteristics
defined
theoretical
griddata
hb1dae <1> <2>
hb1ode
hccurve
Hermitian positive definite factorization
humps
identity matrix
importing
sparse matrix
improving solver performance
incomplete factorization
initial condition
example
initial condition vector
initial condition (ODE)
defined
initial value problem
defined
initial-boundary value problem
inner product
integration
double
numerical
See also ordinary differential equation solvers
interp1
interp2
interp3
interpft
interpn
interpolation
comparing methods
cubic
cubic spline
defined
FFT-based
memory
multidimensional <1> <2>
cubic
linear
nearest neighbor
scattered data
one-dimensional
cubic
cubic spline
linear
nearest neighbor
polynomial
smoothness
speed
three-dimensional
nearest neighbor
tricubic
trilinear
two-dimensional
bicubic <1> <2>
bilinear <1> <2>
nearest neighbor <1> <2>
inv
inverse
isnan
iterative methods
for sparse matrices
for systems of equations
Jacobian matrix (ODE) <1> <2>
evaluated analytically
sparsity pattern
vectorized computation
Jordan Canonical Form
kron
Kronecker tensor product
least squares
linear algebra and matrices
linear interpolation
multidimensional
linear systems of equations
direct methods
iterative methods
sparse
linear transformation
linear-in-the-parameters regression
load
Lobatto IIIa ODE solver
log10
logarithm analysis with a second-order model
lu <1> <2>
LU factorization
for sparse matrices and reordering
magnitude
Maple
mass matrix (ODE) <1> <2>
constant mass matrix
returned by ODE file
mat4bvp
mathematical functions
finding zeros
MATLAB functions for
minimizing <1> <2>
numerical integration
of one variable
finding zeros
of several variables
plotting
quadrature
representing in MATLAB
mathematical operations on sparse matrices
MATLAB
function functions
representing functions
matrices
addition
and linear algebra
diagonal of
dimension compatibility
division
full to sparse conversion <1> <2>
identity
multiplication
orthagonal
subtraction
symmetric
triangular
matrix
characteristic roots
elements
exponentials
iterative methods
multiplication
powers
max
meshgrid <1> <2> <3>
M-files
to represent mathematical functions
min
minimal norm
minimizing functions
of one variable
of several variables
setting minimization options
minimum degree ordering
missing values
monotonic data
for interpolation
Moore-Penrose pseudoinverse
multidimensional arrays
interpolation <1> <2>
multidimensional data gridding
multidimensional interpolation <1> <2>
cubic
linear
nearest neighbor
scattered data
multiple regression
multiplication
matrix
of polynomials
multistep solver (ODE)
multivariate data
NaN
NaNs
removing from data
ndgrid
nearest neighbor interpolation <1> <2> <3> <4>
multidimensional
nnz <1> <2>
nodes
distance between
numbering
nonzero elements
number of
nonzero elements of sparse matrix
maximum number in sparse matrix
storage <1> <2>
values
visualizing with spy plot
nonzeros
norm
Basic Fitting interface
norm, minimal
normalizing data
null
numerical integration
nzmax <1> <2>
ODE. See Ordinary Differential Equations
ode113
description
ode15s <1> <2>
description
ode23
description
ode23s
description
ode23t
description
ode23tb
description
ode45
description
odeget
odephas2
odephas3
odeplot
odeprint
odeset
one-dimensional interpolation <1> <2>
cubic spline
linear
nearest neighbor
ones
one-step solver (ODE)
operator
second difference
operators
colon
optimization
calling sequence changes
practicalities
troubleshooting
optimization code
updating to MATLAB Version 5 syntax
options
minimization
orbitode <1> <2>
Ordinary Differential Equations
coding in MATLAB
definition
passing additional parameters
rewriting for ODE solvers
solvers
Ordinary Differential Equations, solver properties
error tolerance <1> <2>
absolute accuracy
AbsTol
NormControl
relative accuracy
relative to norm of solution
RelTol
event location <1> <2>
Events
Jacobian matrix <1> <2>
Jacobian
JPattern
Vectorized
mass matrix <1> <2>
InitialSlope
Mass
MassSingular
MStateDependence
MvPattern
modifying property structure
ode15s
BDF
MaxOrder
odeset function
querying property structure
solution components for output function
solver output
OutputFcn
OutputSel
Refine
Stats <1> <2>
specifying (overview) <1> <2> <3>
step size <1> <2>
InitialStep
MaxStep
Ordinary Differential Equations, solvers
basic example
nonstiff problem
stiff problem
boundary conditions
calling
different kinds of systems
examples
multistep solver
nonstiff solvers
obtaining solutions at specific times
one-step solver
overview
representing problems
rewriting problem as first-order system
solution array
stability
stiff problems
stiff solvers
syntax, basic
time interval
time span vector
van der Pol example
extra parameters
nonstiff
stiff
orthogonal matrix
orthogonalization
orthonormal columns
outer product
outliers
output properties
BVP solver
ODE solvers
overdetermined systems of simultaneous linear equations
Partial Differential Equations
definition
representing
solver
partial fraction expansion
partial pivoting
pchip
Basic Fitting interface
PDE. See Partial Differential Equations
pdex1
pdex2
pdex3
pdex4
pdex5
performance
improving for solvers
permutations
phase
pinv
pivoting, partial
plotting
mathematical functions
poly <1> <2>
polyder
polyfit <1> <2> <3> <4> <5>
Basic Fitting interface
polynomial
fits to data
interpolation
regression
polynomials
and curve fitting
basic operations
characteristics
derivative of
dividing
evaluating in matrix sense
multiplying
representing
roots
polyval <1> <2> <3> <4>
positive definite factorization
Hermitian
powers
matrix
preconditioner for sparse matrix
preprocessing data <1> <2>
product
dot
inner
outer
property structure (BVP)
creating
modifying
querying
property structure (ODE)
creating
modifying
querying
pseudoinverses
qr
QR factorization <1> <2>
quad <1> <2>
quad8 <1> <2>
quadrature
questions and answers, ODE solvers
different kinds of systems
rand
rank
deficiency <1> <2>
rational format
regression
linear-in-the-parameters
multiple
polynomial
relative accuracy
BVP
ODE
Removing NaNs from data
reorderings
and LU factorization
for sparser factorizations
minimum degree ordering
to reduce bandwidth
representing
polynomial roots
polynomials
problems for ODE solvers
residuals
for exponential data fit
residue
rigid body ODE example
rigidode <1> <2>
roots
roots of polynomial
row vector
for polynomial representation
save
scalar
scattered data
multidimensional tesselation and interpolation
triangulation and interpolation
schur
Schur decomposition
second difference operator, example
shockbvp
singular value decomposition
size
solvers. See ODE solvers
solving linear systems of equations
sparse
sort
sorting data
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
example
spconvert
spdiags
speye <1> <2> <3>
spline
Basic Fitting interface
spones
spparms
sprand
spy
spy plot
sqrtm
stability (ODE solvers)
statistics
analyzing residuals
correlation coefficients
covariance
descriptive
preprocessing data
step size (ODE) <1> <2>
first step
upper bound
stiff ODE
example
stiffness (ODE), defined
storage
for various permutations of sparse matrix
of sparse matrix
sparse and full, comparison
viewing for sparse matrix
subtraction
of matrices
sum <1> <2>
surface plots
to compare interpolation methods
svd
symamd
Symbolic Math Toolbox
symmetric matrix
symmmd <1> <2>
symrcm <1> <2>
systems of equations. See linear systems of equations
systems of ODEs
tesselation
Delaunay
tessellation
Voronoi diagrams
theoretical graph
example
node
three-dimensional interpolation
nearest neighbor
tricubic
trilinear
time
interval (ODE)
transformed data
magnitude
phase
transforms
discrete Fourier
fast Fourier
fft
transpose
complex conjugate
unconjugated complex
triangular factorization
for sparse matrices
triangular matrices
triangulation
closest point searches
Delaunay
Voronoi diagrams
See also tesselation
tricubic interpolation
trilinear interpolation
tsearch
twobvp
two-dimensional interpolation
bicubic
bilinear
nearest neighbor
unconjugated complex transpose
unwrap
updating optimization code to MATLAB Version 5 syntax
van der Pol example
extra parameters
simple, nonstiff
simple, stiff
vdpode <1> <2>
vector
column
initial condition (ODE)
row
time span vector (ODE)
vector products
vectorization
for Jacobian matrix computation (ODE)
visualizing
ODE solver results
sparse matrix
spy plot
voronoi
Voronoi diagrams
multidimensional
voronoin
whos
zeros