...ar spaces and their mappings. The basic divisions of non-linear functional analysis are the following.
...e study of spaces that are locally linear and of Banach manifolds — global analysis.
4 KB (490 words) - 17:11, 7 February 2011
The comparison of algorithms and the analysis of numerical problems in a Bayesian setting, cf. also [[Bayesian approach|B
...worst-case sense over the class $P$. Alternatively, in Bayesian numerical analysis, one puts an [[A priori distribution|a priori distribution]] $\mu$ on the i
6 KB (908 words) - 18:44, 21 March 2024
...orithms have been constructed for the realization of a random search for a global extremum of a function in several variables (see [[#References|[5]]]). Thes
...gn="top">[1]</TD> <TD valign="top"> N.S. Bakhvalov, "Numerical methods: analysis, algebra, ordinary differential equations" , MIR (1977) (Translated from
5 KB (649 words) - 17:24, 7 February 2011
[[Category:Global analysis]]
1 KB (203 words) - 16:38, 17 November 2012
...10/b1100108.png" />) are of no use for an appropriate characterization and analysis of methods which are able to efficiently integrate a stiff problem. Thus th
...zing parameter goes back to [[#References|[a7]]], where it was used in the analysis of multi-step methods. The point is that stiffness is often compatible with
11 KB (1,517 words) - 17:23, 7 February 2011
...t by means of local semantics of statements of the program (so-called flow analysis of the program); checking certain properties of the information collected (
...s are divided into local, the economy part is not larger than a statement; global, the economy part is the entire program; and quasi-local, for which the eco
5 KB (775 words) - 17:05, 7 February 2011
In other words, the problem is to construct a global meromorphic function with locally specified polar singularities.
satisfying the compatibility condition there corresponds a uniquely defined global section of the sheaf $ {\mathcal M} / {\mathcal O} $,
16 KB (2,209 words) - 11:03, 26 March 2023
...braic and analytic geometry, etc. is a frequently used method to construct global objects such as varieties, schemes, differentiable manifolds, vector bundle
and morphisms of schemes between them. Cf. [[Scheme|Scheme]]. Here also global separation properties must be added to obtain a scheme. For vector bundles
4 KB (636 words) - 09:22, 15 January 2024
A very useful fact in analysis is that $C^1$ maps $f$ such that $\left. df\right|_{x_0}$ is invertible at
...the differential is invertible at ''every point'' does not guarantee the ''global invertibility'' of the map. Indeed, a famous example is the exponential map
10 KB (1,719 words) - 16:56, 30 November 2014
...TD valign="top">[a1]</TD> <TD valign="top"> S.S. Chern, "Studies in global analysis and geometry" , ''Studies in Mathematics'' , '''4''' , Math. Assoc. America
2 KB (325 words) - 19:23, 26 March 2024
...M. Shub, "Expanding maps" S.-S. Chern (ed.) S. Smale (ed.) , ''Global analysis'' , ''Proc. Symp. Pure Math.'' , '''14''' , Amer. Math. Soc. (1970) pp. 2
2 KB (337 words) - 19:13, 9 October 2014
...so cannot be a local minimum point of the modulus of $f(z)$. An equivalent global formulation of the maximum-modulus principle is that, under the same condit
|valign="top"|{{Ref|Ah}}||valign="top"| L.V. Ahlfors, "Complex analysis" , McGraw-Hill (1979) pp. 241 {{ZBL|0395.30001}}
4 KB (614 words) - 06:23, 12 October 2023
<TR><TD valign="top">[1]</TD> <TD valign="top"> A. Lichnerowicz, "Global theory of connections and holonomy groups" , Noordhoff (1976) (Translated
...TD valign="top">[a2]</TD> <TD valign="top"> R.O. Wells jr., "Differential analysis on complex manifolds" , Springer (1980)</TD></TR>
3 KB (413 words) - 13:42, 17 March 2023
a finite number of global sections $ s _{1} \dots s _{N} $
by its global sections.)
9 KB (1,307 words) - 20:04, 27 February 2021
==Local and global convergence theory.==
...f$ is decreased as the iteration progresses. There are several variants of global convergence theorems for BFGS and related methods, [[#References|[a9]]], [[
13 KB (1,868 words) - 07:21, 13 February 2024
...D valign="top">[2]</TD> <TD valign="top"> R.O. Wells jr., "Differential analysis on complex manifolds" , Springer (1980)</TD></TR></table>
3 KB (490 words) - 17:46, 4 June 2020
==Local and global theory.==
...see [[Deformation|Deformation]] 1) and 2)). The fundamental methods of the global theory are those of the theory of representable functors and geometric inva
16 KB (2,402 words) - 11:49, 16 December 2019
A global version of the same statement is the following
The global Theorem 2 holds also when $[0,T]$ is replaced by $[-T, 0]$ or $[-T,T]$, by
5 KB (851 words) - 11:10, 30 November 2013
...solution in the space of sequences of bounded functions), and non-standard analysis methods.
...ces of summable functions (or kernel operators, in the quantum case): time-global solutions for general classes of an interaction potential;
10 KB (1,427 words) - 07:38, 7 February 2024
The same analysis has been generalized to the case of a bounded domain in [[#References|[a1]]
...D></TR><TR><TD valign="top">[a5]</TD> <TD valign="top"> J.A. Carrillo, "Global weak solutions of the absorption and reflection-type initial-boundary value
6 KB (900 words) - 08:31, 22 August 2014