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تعداد نتایج: 4579

Holomorphic Maps and Invariant Distances

جزئیات و درخواست

Publisher: Elsevier, 1980-01-01
Pages: 235
Language: en
ISBN_13:9780080871516
ISBN_10:0080871518
Subject: Mathematics

Foundations of Data Science

جزئیات و درخواست

By Avrim Blum, John Hopcroft, Ravindran Kannan
Publisher: Cambridge University Press, 2020-01-23
Pages: 433
Language: en
ISBN_13:9781108485067
ISBN_10:1108485065
Subject: Computers

Complex Function Theory

Second Edition

جزئیات و درخواست

By Donald Sarason
Publisher: American Mathematical Society, 2021-02-16
Pages: 177
Language: en
ISBN_13:9781470463236
ISBN_10:1470463237
Subject: Mathematics

An Initiation to Logarithmic Sobolev Inequalities

جزئیات و درخواست

By Gilles Royer
Publisher: American Mathematical Soc., 2007
Pages: 132
Language: en
ISBN_10:0821844016
ISBN_13:9780821844014
Subject: Mathematics

Introduction to GNU Octave

جزئیات و درخواست

By Jason Lachniet
Publisher: Lulu.com, 2018-11-21
Pages: 156
Language: en
ISBN_13:9780359329649
ISBN_10:0359329640
Subject: Education

Computational Optimal Transport

With Applications to Data Science

جزئیات و درخواست

By Gabriel Peyre, Marco Cuturi
Publisher: Foundations and Trends(r) in M, 2019-02-12
Pages: 272
Language: en
ISBN_10:1680835505
ISBN_13:9781680835502
Subject: Computers

Positive Definite Matrices

جزئیات و درخواست

By Rajendra Bhatia
Publisher: Princeton University Press, 2015-09-01
Pages: 264
Language: en
ISBN_13:9780691168258
ISBN_10:0691168253
Subject: Mathematics

Algebra and Geometry

جزئیات و درخواست

By Alan F. Beardon
Publisher: Cambridge University Press, 2005-05-12
Pages: 340
Language: en
ISBN_13:9781139443494
ISBN_10:1139443496
Subject: Mathematics

Partial Differential Equations

An Introduction

جزئیات و درخواست

By Walter A. Strauss
Publisher: John Wiley & Sons, 2007-12-21
Pages: 467
Language: en
ISBN_13:9780470054567
ISBN_10:0470054565
Subject: Mathematics

Fractals in Probability and Analysis

$A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.$

جزئیات و درخواست

By Christopher J. Bishop, Yuval Peres
Publisher: Cambridge University Press, 2017
Pages: 415
Language: en
ISBN_13:9781107134119
ISBN_10:1107134110
Subject: Mathematics

Linear Algebra and Differential Equations

جزئیات و درخواست

By Alexander Givental
Publisher: American Mathematical Soc., 2001
Pages: 150
Language: en
ISBN_10:0821828509
ISBN_13:9780821828502
Subject: Algebras, Linear

Convex Optimization & Euclidean Distance Geometry

$The study of Euclidean distance matrices (EDMs) fundamentally asks what can be known geometrically given onlydistance information between points in Euclidean space. Each point may represent simply locationor, abstractly, any entity expressible as a vector in finite-dimensional Euclidean space.The answer to the question posed is that very much can be known about the points;the mathematics of this combined study of geometry and optimization is rich and deep.Throughout we cite beacons of historical accomplishment.The application of EDMs has already proven invaluable in discerning biological molecular conformation.The emerging practice of localization in wireless sensor networks, the global positioning system (GPS), and distance-based pattern recognitionwill certainly simplify and benefit from this theory.We study the pervasive convex Euclidean bodies and their various representations.In particular, we make convex polyhedra, cones, and dual cones more visceral through illustration, andwe study the geometric relation of polyhedral cones to nonorthogonal bases biorthogonal expansion.We explain conversion between halfspace- and vertex-descriptions of convex cones,we provide formulae for determining dual cones,and we show how classic alternative systems of linear inequalities or linear matrix inequalities and optimality conditions can be explained by generalized inequalities in terms of convex cones and their duals.The conic analogue to linear independence, called conic independence, is introducedas a new tool in the study of classical cone theory; the logical next step in the progression:linear, affine, conic.Any convex optimization problem has geometric interpretation.This is a powerful attraction: the ability to visualize geometry of an optimization problem.We provide tools to make visualization easier.The concept of faces, extreme points, and extreme directions of convex Euclidean bodiesis explained here, crucial to understanding convex optimization.The convex cone of positive semidefinite matrices, in particular, is studied in depth.We mathematically interpret, for example,its inverse image under affine transformation, and we explainhow higher-rank subsets of its boundary united with its interior are convex.The Chapter on "Geometry of convex functions",observes analogies between convex sets and functions:The set of all vector-valued convex functions is a closed convex cone.Included among the examples in this chapter, we show how the real affinefunction relates to convex functions as the hyperplane relates to convex sets.Here, also, pertinent results formultidimensional convex functions are presented that are largely ignored in the literature;tricks and tips for determining their convexityand discerning their geometry, particularly with regard to matrix calculus which remains largely unsystematizedwhen compared with the traditional practice of ordinary calculus.Consequently, we collect some results of matrix differentiation in the appendices.The Euclidean distance matrix (EDM) is studied,its properties and relationship to both positive semidefinite and Gram matrices.We relate the EDM to the four classical axioms of the Euclidean metric;thereby, observing the existence of an infinity of axioms of the Euclidean metric beyondthe triangle inequality. We proceed byderiving the fifth Euclidean axiom and then explain why furthering this endeavoris inefficient because the ensuing criteria (while describing polyhedra)grow linearly in complexity and number.Some geometrical problems solvable via EDMs,EDM problems posed as convex optimization, and methods of solution arepresented;\eg, we generate a recognizable isotonic map of the United States usingonly comparative distance information (no distance information, only distance inequalities).We offer a new proof of the classic Schoenberg criterion, that determines whether a candidate matrix is an EDM. Our proofrelies on fundamental geometry; assuming, any EDM must correspond to a list of points contained in some polyhedron(possibly at its vertices) and vice versa.It is not widely known that the Schoenberg criterion implies nonnegativity of the EDM entries; proved here.We characterize the eigenvalues of an EDM matrix and then devisea polyhedral cone required for determining membership of a candidate matrix(in Cayley-Menger form) to the convex cone of Euclidean distance matrices (EDM cone); \ie,a candidate is an EDM if and only if its eigenspectrum belongs to a spectral cone for EDM^N.We will see spectral cones are not unique.In the chapter "EDM cone", we explain the geometric relationship betweenthe EDM cone, two positive semidefinite cones, and the elliptope.We illustrate geometric requirements, in particular, for projection of a candidate matrixon a positive semidefinite cone that establish its membership to the EDM cone. The faces of the EDM cone are described,but still open is the question whether all its faces are exposed as they are for the positive semidefinite cone.The classic Schoenberg criterion, relating EDM and positive semidefinite cones, isrevealed to be a discretized membership relation (a generalized inequality, a new Farkas''''''''-like lemma)between the EDM cone and its ordinary dual. A matrix criterion for membership to the dual EDM cone is derived thatis simpler than the Schoenberg criterion.We derive a new concise expression for the EDM cone and its dual involvingtwo subspaces and a positive semidefinite cone."Semidefinite programming" is reviewedwith particular attention to optimality conditionsof prototypical primal and dual conic programs,their interplay, and the perturbation method of rank reduction of optimal solutions(extant but not well-known).We show how to solve a ubiquitous platonic combinatorial optimization problem from linear algebra(the optimal Boolean solution x to Ax=b)via semidefinite program relaxation.A three-dimensional polyhedral analogue for the positive semidefinite cone of 3X3 symmetricmatrices is introduced; a tool for visualizing in 6 dimensions.In "EDM proximity"we explore methods of solution to a few fundamental and prevalentEuclidean distance matrix proximity problems; the problem of finding that Euclidean distance matrix closestto a given matrix in the Euclidean sense.We pay particular attention to the problem when compounded with rank minimization.We offer a new geometrical proof of a famous result discovered by Eckart \& Young in 1936 regarding Euclideanprojection of a point on a subset of the positive semidefinite cone comprising all positive semidefinite matriceshaving rank not exceeding a prescribed limit rho.We explain how this problem is transformed to a convex optimization for any rank rho.$

جزئیات و درخواست

By Jon Dattorro
Publisher: Meboo Publishing USA, 2005
Pages: 776
Language: en
ISBN_13:9780976401308
ISBN_10:0976401304
Subject: Mathematics

The Mathematica GuideBook for Programming

جزئیات و درخواست

By Michael Trott
Publisher: Springer, 2013-12-21
Pages: 1060
Language: en
ISBN_13:9781441985033
ISBN_10:1441985034
Subject: Mathematics

Statistical Mechanics of Lattice Systems

A Concrete Mathematical Introduction

جزئیات و درخواست

By Sacha Friedli, Yvan Velenik
Publisher: Cambridge University Press, 2017-11-23
Pages: 643
Language: en
ISBN_13:9781107184824
ISBN_10:1107184827
Subject: Mathematics

Combinatorics: The Art of Counting

جزئیات و درخواست

By Bruce E. Sagan
Publisher: American Mathematical Soc., 2020-10-16
Pages: 328
Language: en
ISBN_13:9781470460327
ISBN_10:1470460327
Subject: Education

The LLL Algorithm

Survey and Applications

جزئیات و درخواست

By Phong Q. Nguyen, Brigitte Vallée
Publisher: Springer Science & Business Media, 2009-12-02
Pages: 503
Language: en
ISBN_13:9783642022951
ISBN_10:3642022952
Subject: Computers

Alice and Bob Meet Banach

The Interface of Asymptotic Geometric Analysis and Quantum I...

جزئیات و درخواست

By Guillaume Aubrun, Stanisław J. Szarek
Publisher: American Mathematical Society, 2024-07-29
Pages: 439
Language: en
ISBN_13:9781470477967
ISBN_10:1470477963
Subject: Mathematics

Linear Operators and their Spectra

جزئیات و درخواست

By E. Brian Davies
Publisher: Cambridge University Press, 2007-04-26
Pages: 436
Language: en
ISBN_13:9781139464338
ISBN_10:1139464337
Subject: Mathematics

Concentration of Measure for the Analysis of Randomized Algorithms

جزئیات و درخواست

By Devdatt P. Dubhashi, Alessandro Panconesi
Publisher: Cambridge University Press, 2009-06-15
Pages: 213
Language: en
ISBN_13:9781139480994
ISBN_10:1139480995
Subject: Computers

Computing the Continuous Discretely

Integer-Point Enumeration in Polyhedra

جزئیات و درخواست

By Matthias Beck, Sinai Robins
Publisher: Springer, 2015-11-14
Pages: 295
Language: en
ISBN_13:9781493929696
ISBN_10:1493929690
Subject: Mathematics

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