Allgower E.L., Georg K. — Introduction to numerical continuation methods :: Электронная библиотека попечительского совета мехмата МГУ

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Allgower E.L., Georg K. — Introduction to numerical continuation methods

Allgower E.L., Georg K. — Introduction to numerical continuation methods

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Название: Introduction to numerical continuation methods

Авторы: Allgower E.L., Georg K.

Язык:

Рубрика: Математика/Численные методы/Численный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1990

Количество страниц: 388

Добавлена в каталог: 18.02.2005

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Предметный указатель

$C^{\infty}$       see “Smooth”
$G'(\infty)$       see “Jacobian at $\infty$ ”
      cf. preceding (13.3.3)
      cf. (13.3.5)
$\mathbb{C}$ : set of complex numbers, cancellation error      cf. following (7.2.13) following neighborhood preceding section
$\varepsilon$ -perturbation      cf. (12.1.3-4) (14.1.8)
Adjacent simplices      cf. (12.1.7)
Aff(.) symbol for affine hull      cf. (14.1.3)
Affinely independent      cf. (12.1.1)
Angle, measure of curvature      cf. (6.1.7)
Arclength      cf. preceding (1.7) following (5.2.1) preceding preceding
Argmin      see “Minimization”
Asymptotically linear map      cf. (13.1.2)
Augmented Jacobian      cf. (2.1.5)
Automatic pivot      cf. section 13.6
Band structure      cf. (10.3.17)
Barycenter      cf. (12.1.5)
Barycentric coordinates      cf. (12.1.4)
Bezout’s Theorem      cf. (11.6.4)
Bifurcation equation, approximation of      cf. (8.1.7) (8.3.7)—(8.3.9)
Bifurcation point      cf. (8.1.1)
Bifurcation point, detection and approximation      cf. (8.3.1) end
Bifurcation point, simple      cf. (8.1.11)
Boundary condition      cf. following (1.5)
Boundary condition, LS      cf. (11.2.12) (13.1.15)
Boundary condition, Smale’s      cf. (11.4.4) preceding (11.2.12) (11.4.4) (11.5.3) following (11.7.5) (13.1.12) (13.1.16)
Boundary start      cf. (14.1.13)
Boundary termination      cf. (14.1.13)
Branch switching via perturbation      cf. section 8.2
Branch switching via the bifurcation equation      cf. section 8.3
Brouwer fixed point theorem      cf. following (11.1.1) section
Broyden’s formula      cf. (7.1.7) (7.2.3)
Cardinality      see “#”
Cauchy — Riemann      cf. section 11.6 and 11.8
cell      cf. (14.1.4)
cholesky      cf. (10.3.6-7)
Chord method, Newton      cf. preceding (7.1.1) (13.5.1) (15.2.2)
Coercivity condition      cf. (11.7.6) (13.1.22)
Compatible with a triangulation      cf. (13.2.1)
Complementarity problem      cf. (11.7.1) (13.1.22) section (14.4.17) (14.4.44)
Complementary pivoting      cf. (11.7.6) preceding (13.5.1) end of section 14.1
Completely labeled      cf. (12.3.1-3) (14.1.15)
Completely labeled, integer case      cf. (12.5.3)
complex numbers      see “ $\mathbb{C}$ ”
Complexification of a map      cf. preceding (11.8.4)
complexity      cf. preceding (11.7.7)
Condition number      cf. (4.3.1)
Cone construction      cf. (14.4.6)
Conjugate gradient      cf. section 10.3
Contraction rate, Newton      cf. (6.1.1)
Convex function      cf. (13.1.17)
Convex hull      cf. (2.3.1) (12.1.3) (13.1.3)
Convex, uniformly      cf. (10.3.5)
Coordinate      see “[.]”
Corrector procedure      cf. (2.2.3) chapter section (15.2.1)
Coxeter      cf. (12.1.10)
Critical point      cf. section 11.8
Cyclic ordering of vertices      cf. following (12.1.11)
d-homotopy      cf. (11.5.2)
Davidenko      cf. (1.8) (2.1.9)
Defining initial value problem      cf. (2.1.9)
Deflation      cf. (11.5.1)
Degree of a map      cf. following (1.8) following neighborhood
Degree of a polynomial      cf. following (11.6.3)
Delay equation, differential      cf. (P4.1) section
Difference, set-theoretical      see “\”
Dimension of a cell      cf. (14.1.4)
Dimension of a simplex      cf. (2.3.1) (12.1.5)
Distance to curve, measure      cf. (6.1.6)
Door-In-Door-Out-Principle      cf. (12.3.8) (15.4.5)
Edge of a cell      cf. (14.1.5)
Edge of a simplex      cf. (12.1.5)
Embedding method      cf. (1.6)
Error model      cf. section 6.2
Euler — Newton      cf. (3.3.7) chapter section
Extremal points, approximation of      cf. section 9.3
Extremal set      cf. (14.1.5)
Face of a cell      cf. (14.1.5)
Face of a simplex      cf. (2.3.1) (12.1.5)
Facet of a cell      cf. (14.1.4)
Facet of a simplex      cf. (12.1.5)
FLOP      cf. following (16.2.2)
Freudenthal      cf. (12.1.10)
Frobenius norm      cf. (7.1.6)
General position      cf. (12.1.1)
Givens rotations      cf. section 4.2 (10.3.17) preceding
H-center      cf. (12.3.12)
Half-space      cf. (14.1.4)
Hessenberg form      cf. preceding (16.3.3)
hessian      see “Derivative”
Homogeneous part of a polynomial      cf. following (11.6.3)
Homogenization of a polynomial      cf. following (11.6.3)
Homotopy algorithm or method      cf. (1.3)
Homotopy algorithm or method, piecewise linear (PL)      cf. section 13.2 section section
Homotopy level      cf. following (1.5)
Homotopy map      cf. (11.1.1) (11.2.4)
Homotopy, convex or linear      cf. (1.4)
Homotopy, global      cf. (1.5) section
Hyperplane      cf. (14.1.4)
Identity matrix      see “Id”
Implicit function theorem,      cf. following (1.5) preceding following preceding (15.1.1)
Index of a map      cf. (11.5.5) end preceding
Index, Morse      cf. (11.8.2)
Index, PL      cf. section 14.2
Integer labeling      cf. section 12.5
Integers, positive      see “ $\mathbb{N}$ ”
Interior start      cf. (14.1.13)
Interpolation, higher order predictors      cf. section 6.3
Interpolation, PL or affine      cf. preceding (12.1.1) (12.5.4)
Inverse iteration      cf. (8.3.6)
Jacobian      see “Derivative”
Jacobian at 00      cf. (13.1.12)
Kernel, approximation of      cf. (8.3.6)
Labeling matrix      cf. preceding (12.2.6) (12.3.3)
Landau symbol      cf. (3.3.4)
Least change principle      cf. preceding (7.1.6)
Lemke      cf. section 14.3
Leray and Schauder      see “Boundary condition LS”
Leray and Schauder fixed point theorem      cf. (11.1.1)
Lexicographically positive      cf. (12.3.2)
Liapunov — Schmidt reduction      cf. (8.1.3)—(8.1.7)

Line      cf. preceding (14.1.13)
Line search      following 10.3.23)
Linear programming step      see “LP step”
Locally bounded map      cf. (13.1.2)
Locally bounded partition      cf. (13.1.10)
Loop termination      cf. (14.1.13)
LP basis      cf. preceding (15.4.5)
LP step      cf. preceding (12.3.10) section (15.4.5)
LU decomposition or factorization      cf. section 4.5 section
Manifold, PL      cf. (14.1.6)
MAX      see “Minimization”
Maximal point      see “Minimization”
Maximal value      see “Minimization”
Mean value and Taylor’s formula      cf. neighborhood of (5.2.3) (7.1.11) section
Meshsize of a triangulation      cf. (12.6.1) (13.2.3)
MIN      see “Minimization”
Minimal point      see “Minimization”
Minimal value      see “Minimization”
Minimization problem, constrained      cf. (13.1.18)
Moore — Penrose inverse      cf. (3.2.2)
Moving frame      cf. end of section 15.2
Multiple solutions      cf. section 11.5
Multiplicity of a zero point      cf. (11.6.4)
Negative part      cf. (11.7.2)
Neumann series      cf. (5.2.8) (15.5.6)
Newton, global      cf. section 11.4
Newton’s method      cf. following (3.1.1) (3.3.6) (3.4.1) section
Nodes of a triangulation      cf. (12.1.7)
O(.)      see “Landau symbol”
Optimal point      see “Minimization”
Optimal value      see “Minimization”
Order adaptation      cf. section 6.3
Orientation      cf. preceding (2.1.6)
Orientation of PL manifolds      cf. section 14.2 end
Orientation, change      cf. following (8.1.14) (8.1.17)
P-function, uniform      cf. (11.7.10)
Parametrization, local      cf. following (10.2.1)
Perturbation, global      cf. (8.2.1)
Perturbation, local      cf. (8.2.2)
Piecewise-linear (PL) approximation      cf. section 12.2
Piecewise-linear (PL) method      cf. section 2.3 (8.2.1) section section (14.1.17) section
Pivoting by reflection      cf. (12.1.11) (13.3.1) (13.3.3)
Pivoting step      cf. (12.1.9) end
PL approximation of a map      cf. (12.2.1)
PL manifold      cf. (14.1.6)
Polak and Ribiere      cf. (10.3.3)
Polynomial systems      cf. section 11.6
Polynomial time algorithm      cf. preceding (11.7.7) end
Positive definite      cf. (14.3.10)
Positive integers      see “ $\mathbb{N}$ ”
Positive part      cf. (11.7.2)
Preconditioning      cf. neighborhood of (10.3.6)
Predictor, Euler      cf. (2.2.2)
Predictor, variable order      cf. section 6.3
Predictor-corrector (PC) method      cf. following (2.2.3) (3.1.1) preceding (15.3.1)
Primal-dual manifold      cf. (14.4.9)
Primal-dual pair      cf. (14.4.4)
Primary ray      cf. (14.3.8)
Principle minor      cf. following (14.3.9)
Pseudo manifold      cf. (14.1.6)
QL decomposition or factorization      cf. preceding (10.3.10) (16.4.4)
QR decomposition or factorization      cf. section 4.1 section
Quasi-Newton      cf. end of section 7.1 preceding end section
Ray      cf. preceding (14.1.13)
Ray start      cf. (14.1.13)
Ray termination      cf. (14.1.13)
Real numbers      see “ $\mathbb{R}$ ”
Reference matrix      cf. end of section 15.2
Refining manifold      cf. (14.4.8)
Refining triangulation      cf. preceding (13.3.5) preceding
Regular point or value      cf. following (1.5) (2.1.10)
Regular point or value, PL case      cf. (12.2.2) (14.1.7)
Residual algorithm, minimal      cf. end of section 10.3
Resultant      cf. (11.6.6)
Retraction      cf. (13.1.14)
Sard’s theorem,      cf. (11.2.2-3) section preceding preceding preceding preceding
Scalar product      see “ $(.)^{\ast}$ ”
Scaling      cf. section 4.4
Secant equation      cf. (7.1.3)
Secondary bifurcation point      cf. program 4
Secondary ray      cf. (14.3.8)
Segment      cf. preceding (14.1.13)
Self-correcting      cf. (16.2.6)
Separable map      cf. (14.5.1)
Set valued hull      cf. (13.1.3)
Set-valued hull      cf. (13.1.3)
Sherman — Morrison — Formula      cf. (16.2.1)
Simplex, definition of      cf. (2.3.1) (12.1.3)
Singular point or value      cf. (2.1.10)
Singular point or value, PL case      cf. (12.2.2) (14.1.7)
Slab      cf. following (13.2.3)
Slater condition      cf. (13.1.19)
Sperner’s lemma      cf. (14.4.1)
Stability, change in      cf. (9.1.1-2)
Stability, numerical,      cf. end of section 4.4 preceding end end following section chapter
Steplength adaptation      cf. chapter 6
Steplength adaptation, Newton      cf. (9.2.3)
Subgradient      cf. (13.1.17)
Superlinear convergence      cf. (6.2.10) (7.1.8) section
Supporting hyperplane      cf. (14.1.5)
Sylvester matrix      cf. (11.6.6)
t(.)      cf. (2.1.7)
Tangent space of a cell      see “tng(.)”
Tangent vector induced by a matrix      cf. (2.1.7)
Tangent, approximation of      cf. (8.3.10-11)
Taylor’s Formula      cf. neighborhood of (3.4.4) preceding
Thickness, measure of      cf. (15.5.3)
Transverse cell      cf. (14.1.15)
Transverse intersection      cf. preceding (8.1.11) preceding
Transverse simplex      cf. (12.3.7)
Triangulation      cf. (2.3.2) (12.1.6) preceding
Triangulation of a pseudo manifold      cf. (14.1.7)
Truncation error      cf. following (2.3.3) preceding following end neighborhood end end section preceding
Turning points      cf. following (1.6) (9.1.1) (9.3.6) following (11.8.10)
Unit base vector      see “ $e_i$

$e_i$

”
Update method      cf. chapter 7
Upper semi-continuous      cf. (13.1.5)
Variable dimension algorithms      cf. section 14.4
Vector labeling      cf. (12.5.1)
Vertex of a cell      cf. (14.1.4)
Vertex of a simplex      cf. (2.3.1) (12.1.5)
Zero points of a polynomial at $\infty$       cf. (11.6.4)

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