| Mathematics |
 |
- additional parameters
- BVP example <1> <2>
- adjacency matrix
- and graphing
- Bucky ball
- defined
- distance between nodes
- node
- numbering nodes
- airflow modeling
amp1dae demo
- anonymous functions
- representing mathematical functions
- arguments, additional
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 as first-order system
- BVP solver
- basic syntax
- evaluate solution at specific points
- examples
- boundary condition at infinity (
shockbvp)
- Mathieu's Equation (
mat4bvp)
- multipoint terms
- rapid solution changes (
shockbvp)
- singular terms
- initial guess
- multipoint terms
- performance
- representing problems
- singular terms
- unknown parameters
- BVP solver properties
- querying property structure
cat
- sparse operands
- characteristic polynomial of matrix
- characteristic roots of matrix
chol
- sparse matrices
- Cholesky factorization
- sparse matrices
- closest point searches
- Delaunay triangulation
colamd
- minimum degree ordering
colmmd
- column permutation
colperm
- comparing
- sparse and full matrix storage
- complex values in sparse matrix
- computational functions
- applying to sparse matrices
- computational geometry
- multidimensional
- two-dimensional
- contents of sparse matrix
- convex hulls
- multidimensional
- two-dimensional
- convolution
- correlation coefficients
- covariance
- creating
- sparse matrix
- cubic interpolation
- multidimensional
- one-dimensional
- spline
- 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 fitting
- data gridding
- multidimensional
- data. See also
- multivariate data
- statistical data
- univariate data
- DDE
- rewriting as first-order system
- DDE solver
- basic syntax
- discontinuities
- evaluating solution at specific points
- examples
- cardiovascular model (
ddex2)
- straightforward example (
ddex1)
- performance
- representing problems
ddex1 demo
ddex2 demo
- decomposition
- eigenvalue
- Schur
- singular value
- deconvolution
- Delaunay tessellations
- Delaunay triangulation
- closest point searches
- Delay Differential Equations. See DDE
- density
- 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 DAEs
- initial value problems for DDEs
- initial value problems for ODEs
- partial differential equations
- differential-algebraic equations. See DAE
- direct methods
- systems of sparse equations
- discontinuities
- DDE solver
- discrete Fourier transform. See Fourier transforms
- displaying
- sparse matrices
- distance between nodes
- dot product
- eigenvalues
- of sparse matrix
- eigenvectors
- electrical circuits
- DAE example
- Emden's equation
- example
- error bounds
- curve fitting
- error tolerance
- effects of too large (ODE)
- machine precision
- event location (ODE)
- advanced example
- simple example
- exponential curve fitting
eye
- derivation of the name
- sparse matrices
- factorization
- Cholesky
- Hermitian positive definite
- incomplete
- LU
- partial pivoting
- positive definite
- QR
- sparse matrices
- Cholesky
- LU
- triangular
- fast Fourier transform. See Fourier transforms
fem1ode demo
fem2ode demo
- fill-in of sparse matrix
- filtering
- difference equations
find function
- 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
- global variables
gplot
- graph
- characteristics
- defined
hb1dae demo
hb1ode demo
- Hermitian positive definite matrix
- higher-order ODEs
- rewriting as first-order ODEs
iburgersode demo
- identity matrix
ihb1dae demo
- 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
- inner product
- integer mathematics
- integration
- double
- numerical
- triple
- See also differential equations
- integration interval
- DDE
- 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
- sparse matrices
- sparse systems of equations
- 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 (sparse)
- full
- iterative methods (sparse)
- sparse
- linear transformation
load
- sparse matrices
- Lobatto IIIa BVP solver
- LU factorization
- sparse matrices and reordering
mat4bvp demo
mat4bvp demo
- mathematical functions
- as function input arguments
- finding zeros
- minimizing
- numerical integration
- plotting
- representing in MATLAB
- mathematical operations
- sparse matrices
- Mathieu's equation (BVP example)
- matrices
- as linear transformation
- characteristic polynomial
- characteristic roots
- creation
- determinant
- full to sparse conversion
- identity
- inverse
- iterative methods (sparse)
- orthogonal
- pseudoinverse
- rank deficiency
- symmetric
- triangular
- matrix operations
- addition and subtraction
- division
- exponentials
- multiplication
- powers
- transpose
- matrix products
- Kronecker tensor
max
- M-files
- representing mathematical functions
- minimizing mathematical functions
- of one variable
- of several variables
- options
- minimum degree ordering
- Moore-Penrose pseudoinverse
- multidimensional
- data gridding
- interpolation
- 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
- nodes
- distance between
- numbering
- nonstiff ODE examples
- rigid body (
rigidode)
- nonzero elements
- maximum number in sparse matrix
- number in sparse matrix
- sparse matrix
- storage for sparse matrices
- values for sparse matrices
- visualizing for sparse matrices
nonzeros
- normalizing data
- norms
- vector and matrix
- numerical integration
- computing length of curve
- double
- triple
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
- fixed step sizes
- ODE solvers
- algorithms
- Adams-Bashworth-Moulton PECE
- Bogacki-Shampine
- Dormand-Prince
- modified Rosenbrock formula
- numerical 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
- one-step solver
- overview
- performance
- problem size
- representing problems
- sampled data
- stiff problems <1> <2>
- troubleshooting
- one-dimensional interpolation
ones
- sparse matrices
- one-step solver (ODE)
- optimization
- helpful hints
- options parameters
- troubleshooting
- See also minimizing mathematical functions
orbitode demo
- Ordinary Differential Equations. See ODE
- orthogonal matrix
- outer product
- outliers
- removing from statistical data
- output functions
- overdetermined
- rectangular matrices
- overspecified ODE systems
- Partial Differential Equations. See PDE
- partial fraction expansion
- PDE
- defined
- discretized
- PDE examples (MATLAB)
- PDE solver (MATLAB)
- 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
- sparse matrices
- property structure (BVP)
- querying
- pseudoinverse
- of matrix
- QR factorization <1> <2>
quad, quadl functions
- differ from ODE solvers
- quadrature. See numerical integration
rand
- sparse matrices
- rank deficiency
- detecting
- rectangular matrices
- sparse matrices
- rectangular matrices
- identity
- overdetermined systems
- pseudoinverse
- QR factorization
- rank deficient
- singular value decomposition
- underdetermined systems
- regression
- linear-in-the-parameters
- multiple
- polynomial
- reorderings
- for sparser factorizations
- LU factorization
- minimum degree ordering
- reducing bandwidth
- representing
- mathematical functions
- residuals
- analyzing
- 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
- single-precision mathematics
- singular value matrix decomposition
size
- sparse matrices
- solution changes, rapid
- making initial guess
- verifying consistent behavior
- solving linear systems of equations
- full
- sparse
sort
sparse function
- converting full to sparse
- sparse matrix
- advantages
- and complex values
- Cholesky factorization
- computational considerations
- contents
- conversion from full
- creating
- directly
- from diagonal elements
- density
- distance between nodes
- eigenvalues
- fill-in
- importing
- 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
- storage
- for various permutations
- viewing
- triangular factorization
- viewing contents graphically
- viewing storage
- visualizing
- sparse ODE examples
- Brusselator system (
brussode)
spconvert
spdiags
speye
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
- stiff ODE examples
- Brusselator system (
brussode)
- differential-algebraic problem (
hb1dae)
- finite element discretization (
fem1ode)
- van der Pol (
vdpode)
- stiffness (ODE), defined
- storage
- minimizing for ODE problems
- permutations of sparse matrices
- sparse and full, comparison
- sparse matrix
- viewing for sparse matrix
sum
- counting nonzeros in sparse matrix
- sparse matrices
- sunspot periodicity
- calculating using Fourier transforms
symamd
- minimum degree ordering
- symmetric matrix
- transpose
symrcm
- column permutation
- reducing sparse matrix bandwidth
- systems of equations. See linear systems of equations
- tessellations, multidimensional
- Delaunay
- Voronoi diagrams
- theoretical graph
- example
- node
threebvp demo
- three-dimensional interpolation
- transfer functions
- using partial fraction expansion
- transpose
- complex conjugate
- unconjugated complex
- triangular factorization
- 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
- van der Pol example
- simple, nonstiff
- simple, stiff
vdpode demo
- vector products
- dot or scalar
- outer and inner
- vectors
- column and row
- multiplication
- vehicle traffic sample data
- visualizing
- sparse matrix
- visualizing solver results
- BVP
- DDE
- ODE
- PDE
- Voronoi diagrams
- multidimensional
- two-dimensional
- zeros
- of mathematical functions
zeros
- sparse matrices
| References | |
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