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Example

Iterative Method

packed hermitian matrix storage mode

packed symmetric matrix storage mode

packed triangular matrix storage mode

1-norm

2DFT (Discrete Fourier Transform)

3DFT (Discrete Fourier Transform)

Aasen' s method

accuracy estimates of eigenvalues, example

Adams

Adams method

Adams-Moulton's method

adjoint eigenvectors, example

adjoint matrix

ainv= optional argument

Akima interpolant

algebraic-logarithmic singularities

ANSI

arguments, optional subprogram

ARPACK

Base Class, ARPACKBASE

Object Oriented

Type Extension

array permutation

ASCII collating sequence

ASCII values

Avoiding Data Copy to Board

backward difference formulas

band Hermitian storage mode

band storage mode

band symmetric storage mode

band triangular storage mode

Basic Linear Algebra Subprograms

basis functions

bidiagonal matrix

bilinear form

Black-Scholes Equation

BLACS

BLAS

block-cyclic decomposition

boundary conditions

boundary value problem

Brenan

Broyden’s update

B-spline coefficients

B-spline representation

B-splines

Campbell

Cauchy principal value

central differences

changing messages

character arguments

character sequence

character string

character workspace

Chasing a Board

Chebyshev approximation

Chebyshev polynomials

Cholesky

algorithm

decomposition

factorization

method

Cholesky decomposition

Cholesky factorization

circulant linear system

circulant matrices

classical weight functions

codiagonal band hermitian storage mode

codiagonal band symmetric storage mode

coefficient matrix

coefficients

column pivoting

companion matrix

Complex Eigenvectors, real matrices

complex function

complex periodic sequence

complex sparse Hermitian positive definite system

complex sparse system

complex triangular system

complex tridiagonal system

complex vectors

computing

computing eigenvalues, example

Computing Initial Derivatives for DAE Systems

condition number

conjugate gradient algorithm

conjugate gradient method

Constant elasticity of variance, CEV

Constraints

continuous Fourier transform

continuous function

convolution

convolutions, real or complex periodic sequences

coordinate transformation

correlation

cosine

cosine Fourier coefficients

cosine Fourier transform

covariance matrix

CPU time

crossvalidation

cross-validation with weighting, example

cubic spline

cubic spline approximation

cubic spline interpolant

cubic splines

cyclic reduction

cyclic reduction algorithm

cyclical 2D data, linear trend

cyclical data, linear trend

DAE

DAE Solver

DASPG

DASPG routine

data fitting

data points

data, optional

date

decomposition, singular value

degree of accuracy

DENSE_LP

Deprecated Routines

determinant

determinant of A

determinants

determinants

DFT (Discrete Fourier Transform)

Differential Algebraic Equations

differential equations

differential-algebraic equations

differential-algebraic solver

diffusion equation

direct- access message file

direct search complex algorithm

direct search polytope algorithm

discrete Fourier cosine transformation

discrete Fourier sine transformation

discrete Fourier transform

inverse

dot product

double precision

DOUBLE PRECISION types

efficient solution method

eigensystem

complex

complex:Hermitian

real

real:symmetric

eigenvalue

Eigenvalue problem

eigenvectors

generalized complex matrix

generalized real matrix

generalized symmetric

standard complex matrix

standard real matrix

standard symmetric

eigenvalue-eigenvector

decomposition

expansion (eigenexpansion)

eigenvalues

eigenvalues, self-adjoint matrix

eigenvectors

EISPACK

endpoint singularities

equality constraint, least squares

error detection

error handling

errors

Euclidean (2-norm) distance

Euclidean length

even sequence

example

examples

internal write of an array

printing an array

accuracy estimates of eigenvalues

accurate least-squares solution with iterative refinement

analysis and reduction of a generalized eigensystem

complex polynomial equation Roots

computing eigenvalues

computing eigenvectors with inverse iteration

computing generalized eigenvalues

computing the SVD

constraining a spline surface to be non-negative interpolation to data

constraining points using spline surface

convolution with Fourier Transform

cross-validation with weighting

cyclical 2D data with a linear trend

cyclical data with a linear trend

eigenvalue-eigenvector expansion of a square matrix

evaluating the matrix exponential

Generalized Singular Value Decomposition

generating strategy with a histogram

generating with a Cosine distribution

iterative refinement and use of partial pivoting

Laplace transform solution

larger data uncertainty

least squares with an equality constraint

least-squares solution of a rectangular system

linear least squares with a quadratic constraint

Linear ODE:User-Defined Linear Solver:Constraints

matrix inversion and determinant

natural cubic spline interpolation to data

parametric representation of a sphere

periodic curves

polar decomposition of a square matrix

reduction of an array of black and white

ridge regression

running mean and variance

seeding, using, and restoring the generator

selected eigenvectors of tridiagonal matrices

self-adjoint, positive definite generalized eigenvalue problem

several 2D transforms with initialization

several transforms with initialization

shaping a curve and its derivatives

solution of multiple tridiagonal systems

solving a linear least squares system of equations

solving a linear system of equations

solving parametric linear systems with scalar change

sort and final move with a permutation

sorting an array

splines model a random number generator

Swinging Pendulum:Constraints:Index 1 System

system solving with Cholesky method

system solving with the generalized inverse

tensor product spline fitting of data

test for a regular matrix pencil

transforming array of random complex numbers

tridiagonal matrix solving

two-dimensional data fitting

using inverse iteration for an eigenvector

exclusive OR

Expanded Matrix

extended precision arithmetic

factored secant update

factorization, LU

Fast Fourier Transforms

Faure

Faure sequence

Fejer quadrature rule

Feynman-Kac Differential Equation

FFT (Fast Fourier Transform)

finite difference gradient

finite-difference approximation

finite-difference gradient

finite-difference Hessian

finite-difference Jacobian

first derivative

first derivative evaluations

FORTRAN 77

Fortran 90

forward differences

Fourier coefficients

Fourier integral

Fourier transform

Frobenius norm

full storage mode

Fushimi

Galerkin principle

Gauss quadrature

Gauss quadrature rule

Gaussian elimination

Gauss-Kronrod rules

Gauss-Lobatto quadrature rule

Gauss-Radau quadrature rule

Gear’s BDF method

generalized

eigenvalue

feedback shift register (GFSR)

inverse:matrix

generalized inverse

generator

getting started

GFSR algorithm

Givens plane rotation

Givens transformations

globally adaptive scheme

Golub

gradient

Gray code

GSVD

Hadamard product

Hanson

harmonic series

Helmholtz’s equation

Helmholtz's equation

Hermite interpolant

Hermite polynomials

Hermitian positive definite system

Hermitian system

Hessenberg matrix, upper

Hessian

High Performance Fortran

histogram

Horner's scheme

Householder

Householder transformations

hyper-rectangle

IEEE

Index of DAE System

infinite eigenvalues

infinite interval

infinity norm

infinity norm distance

informational errors

initialization, several 2D transforms

initialization, several transforms

initial-value problem

integer options

INTEGER types

integrals

integration

interface block

internal write

interpolation

cubic spline

quadratic

scattered data

inverse

iteration, computing eigenvectors

matrix

matrix:generalized

transform

inverse matrix

isNaN

ISO

iterated integral

Iterative Method

iterative refinement

IVOAM

IVPAG routine

Jacobian

Jenkins-Traub three-stage algorithm

Kershaw

Laguerre’s method

LAPACK

Laplace transform

Laplace transform solution

larger data uncertainty, example

LDU factorization

least squares

least-squares approximation

least-squares problem

least-squares solution

Lebesque measure

Left and right singular vectors

Level 1 BLAS

Level 2 BLAS

Level 3 BLAS

Levenberg-Marquardt algorithm

library subprograms

linear algebraic equations

linear constraints

linear equality/inequality constraints

linear equations

solving

linear least-squares problem

linear least-squares with non-negativity constraints

linear programming problem

linear solutions

linear trend, cyclical 2D data

linear trend, cyclical data

LINPACK

low-discrepancy

LU factorization

LU factorization of A

machine-dependent constants

mathematical constants

matrices

adjoint

complex

complex:band

complex:general

complex:general sparse

complex:Hermitian

complex:rectangular

complex:tridiagonal

complex:upper Hessenberg

copying

covariance

general

Hermitian

inverse

inverse:generalized

inversion and determinant

multiplying

orthogonal

permutation

poorly conditioned

printing

real

real:band

real:general

real:general sparse

real:rectangular

real:sparse

real:symmetric

real:tridiagonal

real:upper Hessenberg

rectangular

sparse:Hermitian

sparse:symmetric

sparse:symmetrical

symmetric

transposing

triangular

unitary

upper Hessenberg

matrix

matrix pencil

matrix permutation

matrix storage modes

matrix/vector operations

matrix-matrix multiply

matrix-matrix solve

matrix-vector multiply

Matrix-Vector Operations

means

Mersenne Twister

message file

Metcalf

method of lines

minimization

minimum degree ordering

minimum point

mistake

Modified Gram-Schmidt algorithm

modified Powell hybrid algorithm

MOLCH

monic polynomials

Moore-Penrose

MPI

Muller’s method

multiple right sides

multivariate functions

multivariate quadrature

naming conventions

NaN (Not a Number)

Newton algorithm

Newton method

Newton' s method

noisy data

nonadaptive rule

nonlinear equations

nonlinear least-squares problem

nonlinear programming

norm

Normal Matrix

normalize

not-a-knot condition

Notes for BLAS Using NVIDIA

Number of Installed Boards

numerical differentiation

NVIDIA

odd sequence

odd wave numbers

optional argument

optional data

optional subprogram arguments

order one or two

ordinary differential equations

ordinary eigenvectors, example

orthogonal

orthogonal matrix

orthogonalized

overflow

page length

page width

parameters

parametric linear systems with scalar change

parametric systems

partial differential equations

Partial Expansion

partial pivoting

PBLAS

performance index

periodic boundary conditions

permutation

Petzold

physical constants

piecewise polynomial

piecewise-linear Galerkin

pivoting

partial

row and column

symmetric

plane rotation

plots

Poisson solver

Poisson's equation

polar decomposition

polynomial

interpolation

polynomial curve

prime factors

printing

printing an array, example

printing arrays

printing results

private message files

programming conventions

pseudorandom number generators

pseudorandom numbers

PV-WAVE

QR algorithm

QR decomposition

QR factorization

quadratic interpolation

quadratic polynomial interpolation

quadrature formulas

quadrature rule

quadruple precision

quasi-Monte Carlo

quasi-Newton method

quintic polynomial

radial-basis functions

random complex numbers, transforming an array

random number generator

random number generators

random numbers

rank-2k update

rank-k update

rank-one matrix

rank-one matrix update

rank-two matrix update

rational weighted Chebyshev approximation

READ_MPS

real numbers, sorting

real periodic sequence

real sparse symmetric positive definite system

real symmetric definite linear system

real symmetric positive definite system

real symmetric system

real triangular system

real tridiagonal system

REAL types

real vectors

record keys, sorting

rectangular domain

rectangular grid

recurrence coefficients

Reducing the Index

reduction

References

regularizing term

Reid

required arguments

reserved names

reverse communication

revised simplex method

ridge regression

Rodrigue

row and column pivoting

row vector, heavily weighted

Runge-Kutta-order method

Runge-Kutta-Verner fifth-order method

Runge-Kutta-Verner sixth-order method

ScaLAPACK

scattered data

scattered data interpolation

Schur form

search

second derivative

self-adjoint

eigenvalue problem

linear system

matrix

matrix:eigenvalues

matrix:tridiagonal

semi-infinite interval

sequence

serial number

simplex algorithm

sine

sine Fourier coefficients

sine Fourier transform

single precision

SINGLE PRECISION options

Single Program, Multiple Data

Singular Value Decomposition

ARPACK

singular value decomposition (SVD)

singularity

singularity points

smooth bivariate interpolant

smoothing

smoothing formulas

smoothing spline routines

solvable

solving

solving linear equations

sorting

sorting an array, example

Sparse

sparse linear programming

Sparse Matrix Computations, Examples

sparse matrix storage mode

Sparse Matrix, Complex

Sparse Matrix, Real

sparse system

spline approximation

spline interpolant

spline knot sequence

splines

square matrices

eigenvalue-eigenvector expansion

polar decomposition

square root

Stiff Solver

Sturm-Liouville problem

subprograms

SVD

SVD Example

SVRGN

Switching from Fortran to NVIDIA BLAS

Switchover Size

symmetric Markowitz strategy

Symmetric Matrix

system of ordinary differential equations

tensor product splines

tensor-product B-spline coefficients

tensor-product B-spline representation

tensor-product spline

tensor-product spline approximant

tensor-product spline interpolant

terminal errors

third derivative

time

Timing

Toeplitz linear system

Toeplitz matrices

traceback

transfer

transportation problem

transpose

tridiagonal

triple inner product

two-dimensional data fitting

unconstrained minimization

underflow

uniform (0, 1) distribution

uniform mesh

unitary matrix

univariate functions

univariate quadrature

upper Hessenberg matrix

user errors

user interface

User-Defined Linear Solver

user-supplied function

user-supplied gradient

Using LAPACK, LINPACK, and EISPACK

using library subprograms

Van Loan

variable knot B-spline

variable order

variable order Adams method

variances

variational equation

vectors

version

workspace allocation

World Wide Web

zero of a real function

zero of a real univariate function

zeros of a polynomial

zeros of a univariate complex function

zeros of the polynomial