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Barycentre method for solving distance equations / X. Shuqiang in Survey review, vol 48 n° 348 (May 2016)
Titre : Barycentre method for solving distance equations Type de document : Article/Communication Auteurs : X. Shuqiang, Auteur ; Y. Yuanxi, Auteur ; D. Yamin, Auteur Année de publication : 2016 Article en page(s) : pp 188 - 194 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Mathématique
[Termes descripteurs IGN] algorithme de Gauss-Newton
[Termes descripteurs IGN] barycentre
[Termes descripteurs IGN] distance
[Termes descripteurs IGN] équation
[Termes descripteurs IGN] itération
[Termes descripteurs IGN] méthode des moindres carrésRésumé : (auteur) When iteratively solving the distance equations, the Newton’s method has quadratic convergence but it requires the second-order derivatives. The Gauss–Newton’s method needs no information about the second-order derivatives but it may fail without the line search strategy. A simple method called barycentre method is proposed to locally solving the distance equations without the Hessian matrix, the matrix inversion and the line search strategy. The geometrical meaning of the non-linear least-squares solution of the distance equations is revealed that it is the barycentre of a particle system composed of the observational weights at the endpoints of observed distance vectors. By the geometrical meaning of the non-linear least squares, the authors structure an iterative equation to solve the distance equation, and then the convergence and the computational complexity of the method proposed is discussed. It shows that the barycentre method is a conservatively steepest decent method to guarantee the convergence and this method has good performances for solving well-conditioned problems. Ultimately, the method proposed is applied to well-condition and ill-posed positioning equations and the main results are verified. Numéro de notice : A2016-275 Thématique : MATHEMATIQUE/POSITIONNEMENT Nature : Article DOI : 10.1179/1752270615Y.0000000020 En ligne : http://doi.org/10.1179/1752270615Y.0000000020 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=80824
in Survey review > vol 48 n° 348 (May 2016) . - pp 188 - 194[article]
Titre : Brownian motion, martingales, and stochastic calculus Type de document : Guide/Manuel Auteurs : Jean-François Le Gall, Auteur Editeur : Springer International Publishing Année de publication : 2016 Importance : 273 p. Format : 16 x 24 cm ISBN/ISSN/EAN : 978-3-319-31089-3 Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Mathématique
[Termes descripteurs IGN] chaîne de Markov
[Termes descripteurs IGN] fonction harmonique
[Termes descripteurs IGN] mouvement brownien
[Termes descripteurs IGN] probabilités
[Termes descripteurs IGN] stochastiqueRésumé : (éditeur) This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô's formula, the optional stepping theorem and Girsanov's theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested in such developments. Beginning graduate or advanced undergraduate students will benefit from this detailed approach to an essential area of probability theory. The emphasis is on concise and efficient presentation, without any concession to mathematical rigor. The material has been taught by the author for several years in graduate courses at two of the most prestigious French universities. The fact that proofs are given with full details makes the book particularly suitable for self-study. The numerous exercises help the reader to get acquainted with the tools of stochastic calculus. Numéro de notice : 26586 Thématique : MATHEMATIQUE Nature : Manuel En ligne : https://doi.org/10.1007/978-3-319-31089-3 Format de la ressource électronique : URL Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=95220
Titre : Introduction to partial differential equations Type de document : Guide/Manuel Auteurs : David Borthwick, Auteur Editeur : Springer International Publishing Année de publication : 2016 Importance : 636 p. Format : 18 x 26 cm ISBN/ISSN/EAN : 978-3-319-48936-0 Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Mathématique
[Termes descripteurs IGN] équation de Laplace
[Termes descripteurs IGN] équation différentielle
[Termes descripteurs IGN] équation linéaire
[Termes descripteurs IGN] onde acoustique
[Termes descripteurs IGN] série de Fourier
[Termes descripteurs IGN] transformation de FourierRésumé : (éditeur) This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, and elsewhere. The exposition carefully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. Extensive exercise sets appear at the end of almost every subsection, and include straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and proofs, challenging projects both computational and conceptual, and supplementary material that motivates the student to delve further into the subject.
No previous experience with the subject of partial differential equations or Fourier theory is assumed, the main prerequisites being undergraduate calculus, both one- and multi-variable, ordinary differential equations, and basic linear algebra. While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to form the core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, symmetry and similarity, the Maximum Principle, financial models, dispersion and solitons, Huygens'. Principle, quantum mechanical systems, and more make this text well attuned to recent developments and trends in this active field of contemporary research. Numerical approximation schemes are an important component of any introductory course, and the text covers the two most basic approaches: finite differences and finite elements.Note de contenu : 1- Introduction
2- Preliminaries
3- Conservation Equations and Characteristics
4- The Wave Equation
5- Separation of Variables
6- The Heat Equation
7- Function Spaces
8- Fourier Series
9- Maximum Principles
10- Weak Solutions
11- Variational Methods
12- Distributions
13- The Fourier TransformNuméro de notice : 25868 Thématique : MATHEMATIQUE Nature : Manuel DOI : 10.1007/978-3-319-48936-0 En ligne : https://doi.org/10.1007/978-3-319-48936-0 Format de la ressource électronique : URL Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=95528
Titre : Methods of Mathematical Modelling : Continuous Systems and Differential Equations Type de document : Guide/Manuel Auteurs : Thomas Witelski, Auteur ; Mark Bowen, Auteur Editeur : Springer International Publishing Année de publication : 2015 Importance : 324 p. Format : 16 x 24 cm ISBN/ISSN/EAN : 978-3-319-23042-9 Note générale : bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Mathématique
[Termes descripteurs IGN] analyse mathématique
[Termes descripteurs IGN] calcul différentiel
[Termes descripteurs IGN] calcul variationnel
[Termes descripteurs IGN] équation différentielle
[Termes descripteurs IGN] équation linéaire
[Termes descripteurs IGN] modèle mathématique
[Termes descripteurs IGN] série de Fourier
[Termes descripteurs IGN] variableRésumé : (éditeur) This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences. Note de contenu : Part I- Formulation of Models
1- Rate equations
2- Transport equations
3- Variational principles
4- Dimensional scaling analysis
Part II- Solution Techniques
5- Self-similar scaling solutions of differential equations
6- Perturbation methods
7- Boundary layer theory
8- Long-wave asymptotics for PDE problems
9- Weakly-nonlinear oscillators
10- Fast/slow dynamical systems
11- Reduced models for PDE problems
Part III- Case Studies
12- Modelling in applied fluid dynamics
EpilogueNuméro de notice : 25830 Thématique : MATHEMATIQUE Nature : Manuel En ligne : https://doi.org/10.1007/978-3-319-23042-9 Format de la ressource électronique : URL Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=95152
Titre : Reconstruction of trees with cylindrical quadrics and radial basis functions Type de document : Article/Communication Auteurs : Jules Morel, Auteur ; Alexandra Bac, Auteur ; Cédric Vega Congrès : MMT 2015, 9th International Symposium on Mobile Mapping Technology (9 - 11 décembre 2015; Sydney, Australie), Commanditaire Editeur : Kensington (Australie) : University of New South Wales Année de publication : 2015 Importance : pp 53 - 59 Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Mathématique
[Termes descripteurs IGN] arbre (flore)
[Termes descripteurs IGN] fonction de base radiale
[Termes descripteurs IGN] reconstruction d'objetNuméro de notice : C2015-053 Thématique : FORET/IMAGERIE/MATHEMATIQUE Nature : Communication nature-HAL : ComSansActesPubliés-Unpublished DOI : sans Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=84572 PermalinkPermalinkPermalinkPermalinkPermalinkPermalinkPermalinkPermalinkPermalinkPermalink
