| Mathematics |
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abs
- absolute accuracy (BVP)
- absolute accuracy (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 problem
- defined
- Boundary value problems
- passing additional known parameters <1> <2>
- boundary value problems
- Brusselator system (ODE example)
brussode <1> <2>
- Buckminster Fuller dome
- Bucky ball
burgersode
- BVP 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
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)
- columns
- 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)
contour
- contour plots, to compare interpolation methods
conv
- convex hull
convhull
- 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
- Harwell-Boeing format
- monotonic
- multivariate
- pre-processing
- 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 triangulation
- closest point searches
- 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, See ODE solvers <1> <2>
- 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 <1> <2>
- eigenvalue
- decomposition
- eigenvalues
- of sparse matrix
- eigenvector
- error
- bound, for data fit
- tolerance (BVP) <1> <2>
- tolerance (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 <1> <2>
- 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
- 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.<it> See<df> 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
- Harwell-Boeing data format
hb1dae <1> <2>
hb1ode
hccurve
humps
- identity matrix
- importing
- sparse matrix
- improving solver performance
- incomplete factorization
- initial condition
- defined
- example
- initial condition vector
- 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
- 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
- multiple regression
- multiplication
- matrix
- of polynomials
- multistep solver (ODE)
- multivariate data
NaN
ndgrid <1> <2>
- 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
- norm, minimal
- normalizing data
null
- numerical integration
nzmax <1> <2>
- ODE 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
- ODE 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
- 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
- cubic spline
- linear
- nearest neighbor
ones
- one-step solver (ODE)
- operator
- second difference
- operators
- colon
- optimization
- practicalities
- troubleshooting
- options
- minimization
orbitode <1> <2>
- Ordinary Differential Equation solvers. See ODE solvers <1> <2>
- Ordinary Differential Equations
- coding in MATLAB
- defined
- passing additional parameters
- rewriting for ODE solvers
- orthogonal matrix
- orthogonalization
- orthonormal columns
- outer product
- outliers
- output properties, BVP solver
- output properties, ODE solvers
- overdetermined systems of simultaneous linear equations
- partial fraction expansion
- partial pivoting
- 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>
- 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
- powers
- matrix
- preconditioner for sparse matrix
- pre-processing 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)
- relative accuracy (ODE)
- 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
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>
spones
spparms
sprand
spy
- spy plot
sqrtm
- stability (ODE solvers)
- statistics
- analyzing residuals
- correlation coefficients
- covariance
- descriptive
- pre-processing 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
- 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
- tricubic interpolation
- trilinear interpolation
tsearch
twobvp
- two-dimensional interpolation
- bicubic
- bilinear
- nearest neighbor
- unconjugated complex transpose
unwrap
- 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
whos
zeros
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