Index

ndigit

msaitr

debug.h

msaupd

arpack_state

Check Pointing ARPACK

ex-sym.doc

An Example for a

ndigit

logfil

msaitr

__aupd

__eupd

Reverse Communication Structure for

OP

dsaupd

Computational Modes for Real

dseupd

Post-Processing for Eigenvectors Using dseupd

dneupd

Post-Processing for Eigenvectors Using dneupd

znaupd

Computational Modes for Complex

zneupd

Post-Processing for Eigenvectors Using zneupd

${\bf M}$ -inner product

_gemv

Computational Routines

XYaupd

XYeupd

XYaup2

Xgetv0

XYaitr

Xneigh

[s,d]seigt

XYgets

[s,d]Yconv

XYapps

Xortc

[s,d]ortr

[s,d]laqrb

[s,d]stqrb

XYaupd

XYaupd

XYaup2

XYaitr

XYaitr

Xgetv0

Xgetv0

[s,d]neigh

Xneigh

[s,d]laqrb

Xneigh

[s,d]lahqr

Xneigh

[c,z]lahqr

Xneigh

[c,z]neigh

Xneigh

[c,z]trevc

Xneigh

[s,d]seigt

[s,d]seigt

[s,d]stqrb

[s,d]seigt

[s,d]stqr

[s,d]seigt

[s,d]Yconv

[s,d]Yconv

[c,z]naup2

[s,d]Yconv

XYapps

XYapps

XYeupd

XYeupd

Xtrsen

XYeupd

Xtrevc

XYeupd

Xtrmm

XYeupd

Xhseqr

Xlahqr

Xtrsen

[s,d]steqr

ctrevc

strevc

Xlahqr

Xgeqr2

sorm2r

cunm2r

Xlascl

Xlanhs

Xlacpy

Xlamch

[s,d]labad

[s,d]lapy2

Xlartg

[s,d]larfg

[s,d]larf

Xlaset

BLAS

Xgemv

[s,d]ger

[c,z]geru

Xaxpy

Xscal

[s,d]dot

[c,z]dotc

[cs,zd]scal

[s,d]nrm2

[sc,dz]nrm2

Xcopy

Xswap

Reverse Communication Interface

XYaup2

COMMON

[s,d]Yconv

ido

Reverse Communication Interface

LR

SR

LI

SI

LM

LI

SI

SR

dssimp

Directory Structure and Contents

dssimp

XsdrvY

dsdrv1

dsdrv2

dsdrv3

dsdrv4

dsdrv5

dsdrv6

Cayley Transformation Mode

dndrv1

Standard Mode

dndrv2

Shift-Invert Mode

dndrv3

Regular Inverse Mode

dndrv4

Spectral Transformations for Non-symmetric

dndrv5

Spectral Transformations for Non-symmetric

dndrv6

Spectral Transformations for Non-symmetric

zndrv1

Standard Mode

zndrv2

[s,d]seigt

[s,d]Yconv

Xneigh

accuracy

checking: Postprocessing and Accuracy Checking | Postprocessing and Accuracy Checking | Post-processing and Accuracy Checking | Accuracy checking

Arnoldi

block: Block Methods
compressed factorization: Implicit Restarting
factorization: The Arnoldi Factorization
orthogonal vectors: The Arnoldi Factorization
relation: The Arnoldi Factorization
vectors: The Arnoldi Factorization

ARPACK

Amount of disk storage: Installation
Availability by ftp: Availability
Availability by URL: Availability
Availability in ScaLAPACK: Availability
Compliance with ANSI standard Fortran: Expected Performance
Contributions to: Contributed Additions
Expected performance: Expected Performance
installation: Installation
library: Directory Structure and Contents
makefile: Installation
Parallel: P_ARPACK
subroutines: ARPACK subroutines

availability

Availability

B-orthogonal

Computational Routines

backward error

basis

standard: Structure of the Eigenvalue

BLACS

Dependence on LAPACK and | Computational Routines

BLAS

used by ARPACK: BLAS routines used by

blockArnoldi

Block Methods

bulge chases of QR

characteristic polynomial

Tracking the progress of | Check Pointing ARPACK

Chebyshev

polynomial: XYaup2

check pointing

choice of shifts

Using the Computational Modes

exact ones: Implicit Restarting

Cholesky factorization of ${\bf M}$

${\bf M}$ is Hermitian Positive

classical Gram-Schmidt

XYaitr

complex

Hermitian: Band Drivers

computing eigenvectors

dseupd: Post-Processing for Eigenvectors Using dseupd
dneupd: Post-Processing for Eigenvectors Using dneupd
zneupd: Post-Processing for Eigenvectors Using zneupd

computing interior eigenvalues

computing Schur vectors

dneupd: Post-Processing for Eigenvectors Using dneupd
zneupd: Post-Processing for Eigenvectors Using zneupd

condition number

2-norm condition estimator: The SVD Drivers
of a matrix: The SVD Drivers

Contents of ARPACK

Directory Structure and Contents

contribution

Contributed Additions

Contributions to ARPACK

Contributed Additions

convention

naming: ARPACK subroutines

convergence of IRAM

XYaup2

convex hull

cost

computational: Computational Routines
of implicit restart: Using the Computational Modes

data

type: Naming Conventions, Precisions and | ARPACK subroutines

data structure

Identify OP and B

Data types

debugging

Tracking the progress of

Debugging capability

defective

deflation

departure from normality

DGKS

correction: The Arnoldi Factorization | XYaitr

direct methods

factoring shift-invert: Shift and Invert Spectral

direct residual

directories of ARPACK

ARMAKES: Directory Structure and Contents
BAND: Directory Structure and Contents
BLAS: Directory Structure and Contents
COMPLEX: Directory Structure and Contents
DOCUMENTS: Directory Structure and Contents
EXAMPLES: Directory Structure and Contents
LAPACK: Directory Structure and Contents
NONSYM: Directory Structure and Contents
SRC: Directory Structure and Contents
SVD: Directory Structure and Contents
SYM: Directory Structure and Contents
UTIL: Directory Structure and Contents

dominant eigenvalue

driver routines

example: Templates and Driver Routines
simple: Getting Started

drivers

band: Band Drivers
complex: Complex Drivers
non-symmetric: Real Nonsymmetric Drivers
selection: Selecting a Symmetric Driver
SVD: The SVD Drivers
symmetric: Symmetric Drivers

eigenpair

eigenvalue problems

generalized: Generalized Eigenvalue Problem | Generalized Nonsymmetric Eigenvalue Problem | Generalized Eigenvalue Problems
standard: Setting up the problem

eigenvalues

accuracy

clustered

Post-Processing for Eigenvectors Using dneupd

conjugate pair

distinct

dominant

extremal

Shift and Invert Spectral | Structure of the Spectral

infinite

interior

largest

imaginary part: Standard Mode
magnitude: Standard Mode
real part: Standard Mode

largest

multiple

non-clustered

sensitivity

smallest

magnitude: Standard Mode
imaginary part: Standard Mode
real part: Standard Mode

smallest

spurious

wanted

well separated

eigenvector

accuracy: Stopping Criterion
left: Structure of the Eigenvalue
normalization: Post Processing for Eigenvalues | Post-Processing for Eigenvectors Using dseupd | Post-Processing for Eigenvectors Using dneupd | Post-Processing for Eigenvectors Using zneupd | XYeupd
purification: Post-Processing for Eigenvectors Using dseupd | Post-Processing for Eigenvectors Using dneupd | Post-Processing for Eigenvectors Using zneupd
right: Structure of the Eigenvalue | Krylov Subspaces and Projection
sensitivity: Stopping Criterion
simple: Structure of the Eigenvalue

eigenvectors

complex eigenvectors in real arithmetic: Post-Processing for Eigenvectors Using dneupd
purification: Eigenvector/Null-Space Purification

error

backward: Stopping Criterion
residual: Eigenvector/Null-Space Purification

exact shifts

example driver for using dsaupd

An Example for a

execution

rate of: Computational Routines

extremal eigenvalues

filter

Fortran77

Krylov Subspaces and Projection

Galerkin condition

GMRES

Hessenberg decomposition

Hessenberg matrix

ill-conditioned

mass matrix: The Generalized Eigenvalue Problem

implicit restart

implicit shifts

exact: Initial Parameter Settings

Improving convergence

with spectral transformations: Shift and Invert Spectral

include

include files

Expected Performance

indefinite linear systems

Shift and Invert Spectral | The Generalized Eigenvalue Problem

Initial parameter settings

for dsaupd: Initial Parameter Settings

initial vector

generating of: Xgetv0

inner product

weighted: Shift and Invert Spectral

invariant subspace

Introduction to ARPACK | The Implicitly Restarted Arnoldi

sensitivity: Structure of the Eigenvalue | Stopping Criterion

IRAM

convergence rate: XYaup2

IRLM

Krylov Subspaces and Projection

Iterative methods

shift-invert: Shift and Invert Spectral

Krylov

block subspace: Block Methods
invariant subspace: Krylov Subspaces and Projection
projection methods: Krylov Subspaces and Projection
subspace: Krylov Subspaces and Projection

Krylov methods

link with power method: Krylov Subspaces and Projection

Lanczos

Dependence on LAPACK and | Computational Routines

block method: Eigenvector/Null-Space Purification
factorization: The Arnoldi Factorization
orthogonal vectors: The Arnoldi Factorization
vectors: The Arnoldi Factorization

LAPACK

used by ARPACK: LAPACK routines used by

loss of orthogonality

Structure of the Spectral | Structure of the Spectral

M-Arnoldi process

M-inner product

Shift and Invert Spectral | Cayley Transformation Mode

machine precision

Stopping Criterion | Shift and Invert Spectral | Stopping Criterion | [s,d]Yconv

matrix

Hessenberg: Structure of the Eigenvalue
Jordan form: Structure of the Eigenvalue
mass: The Generalized Eigenvalue Problem
normal: Structure of the Eigenvalue
overlap: The Generalized Eigenvalue Problem
Schur form: Structure of the Eigenvalue
stiffness: The Generalized Eigenvalue Problem | The Generalized Eigenvalue Problem
tridiagonal: Structure of the Eigenvalue

matrix factorization

direct: Getting Started with ARPACK

message passing

mode

Buckling: Buckling Mode
Cayley: Cayley Transformation Mode
regular-inverse: Regular Inverse Mode | Regular Inverse Mode | Regular Inverse Mode
shift-invert: Shift-Invert Mode | General Shift-Invert Spectral Transformation
standard: Standard Mode

modes, computational

Buckling: Using the Computational Modes
Cayley: Using the Computational Modes
complex: Computational Modes for Complex
non-symmetric: Computational Modes for Real
regular: Using the Computational Modes
regular-inverse: Using the Computational Modes
shift-invert: Using the Computational Modes
symmetric: Computational Modes for Real

MPI

multiplicity

algebraic: Structure of the Eigenvalue
geometric: Structure of the Eigenvalue
missed: Stopping Criterion | Other Variables | Other Variables | Other Variables | Modify other variables if

Naming conventions

Netlib

Availability

non-clustered eigenvalues

notation

orthogonality

Arnoldi vectors: The Arnoldi Factorization
Lanczos vectors: The Arnoldi Factorization

parallel ARPACK

polynomial

acceleration: Implicit Restarting
characteristic: Structure of the Eigenvalue
Chebyshev: XYaup2
filter: Implicit Restarting
implicitly applied: Implicit Restarting

polynomial restarting

Postprocessing and Accuracy Checking | Postprocessing and Accuracy Checking | Post-processing and Accuracy Checking

post-processing

power method

precision

Precision of data

Trouble Shooting and Problems

Problems with ARPACK

projection methods

Krylov: Krylov Subspaces and Projection

purging

Eigenvector/Null-Space Purification

purification of eigenvectors

QR

algorithm: Structure of the Eigenvalue
as subspace iteration: Implicit Restarting
factorization: Structure of the Eigenvalue
iteration: Structure of the Eigenvalue | XYapps
truncated iteration: Implicit Restarting | Implicit Restarting

range

Xgetv0

Rayleigh quotient

Research Funding of ARPACK

residual: The Arnoldi Factorization

README

Availability

Research Funding of ARPACK

restarting

Important Features | Reverse Communication Interface | The Reverse Communication Interface | The Reverse Communication Interface

exact shifts: Implicit Restarting
filtering: Implicit Restarting
implicitly: Implicit Restarting
polynomial: Implicit Restarting

reverse communication

flag: Initial Parameter Settings
shift-invert transformation: Reverse Communication Structure for

Ritz

estimate: The Arnoldi Factorization
value: Krylov Subspaces and Projection
vector: Krylov Subspaces and Projection

routines

computational: Computational Routines

Schur decomposition

The Generalized Eigenvalue Problem

partial: Structure of the Eigenvalue | Krylov Subspaces and Projection

self-adjoint

semi-inner product

sep

Using the Computational Modes

Setting nev and ncv

Setting nev and ncv

Setting up the problem

shift-invert

shifts

exact: Implicit Restarting
implicit: ARPACK subroutines

similar

similarity transformation

Directory Structure and Contents

SIMPLE

simple driver

symmetric eigenvalue problem: An Example for a

simple driver dssimp

An Example for a

singular

Structure of the Spectral

singular mass matrix

singular value decomposition

The Singular Value Decomposition

singular vectors

left: The Singular Value Decomposition
right: The Singular Value Decomposition

spectral enhancement

Shift and Invert Spectral | Structure of the Spectral | Spectral Transformations for Non-symmetric

spectral transformation

deciding: Shift and Invert Spectral
enhance convergence: Structure of the Spectral
factorization with a direct method: Shift and Invert Spectral
linear systems: Shift and Invert Spectral
matrix factorization: Shift and Invert Spectral

spectrum

Setting the Starting Vector

standard eigenvalue problem

${\bf M}$ is Hermitian Positive

starting vector

stopping criterion

Ritz estimate: Stopping Criterion
symmetric eigenvalue problems: Stopping Criterion

subroutines of ARPACK

auxiliary: ARPACK subroutines

subspace

invariant: Structure of the Eigenvalue

subspace iteration

The Singular Value Decomposition

as QR iteration: Implicit Restarting

SVD

templates

simple: Getting Started

three term recurrence

tridiagonal matrix

Trouble Shooting and Problems

Trouble shooting ARPACK

unitary

matrix: Structure of the Eigenvalue

variable

problem dependent: Modify the Problem Dependent

variables

other: Other Variables | Other Variables | Other Variables | Modify other variables if
problem dependent: Modify the Problem Dependent | Modify the Problem Dependent | Modify problem dependent variables

well separated eigenvalues