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Электронная библиотека Попечительского совета механико-математического факультета Московского государственного университета
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Allgower E.L., Georg K. - Introduction to numerical continuation methods |
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Предметный указатель |
see 'Smooth'
see 'Jacobian at '
cf. preceding (13.3.3)
cf. (13.3.5)
: set of complex numbers, cancellation error cf. following (7.2.13) following neighborhood preceding section
-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 ''
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 ''
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 ''
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 ''
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 ''
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 ''
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 cf. (11.6.4)
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