Format:
Online-Ressource (XXVIII, 909p. 60 illus, digital)
Edition:
Second
ISBN:
9780387682761
,
128297355X
,
9781282973558
Series Statement:
Springer Series in Statistics
Content:
Introduction -- Doubly Stochastic Matrices -- Schur-Convex Functions -- Equivalent Conditions for Majorization -- Preservation and Generation of Majorization -- Rearrangements and Majorization -- Combinatorial Analysis -- Geometric Inequalities -- Matrix Theory -- Numerical Analysis -- Stochastic Majorizations -- Probabilistic, Statistical, and Other Applications -- Additional Statistical Applications -- Orderings Extending Majorization -- Multivariate Majorization -- Convex Functions and Some Classical Inequalities -- Stochastic Ordering -- Total Positivity -- Matrix Factorizations, Compounds, Direct Products, and M-Matrices -- Extremal Representations of Matrix Functions.
Content:
This book’s first edition has been widely cited by researchers in diverse fields. The following are excerpts from reviews. “Inequalities: Theory of Majorization and its Applications” merits strong praise. It is innovative, coherent, well written and, most importantly, a pleasure to read. … This work is a valuable resource!” (Mathematical Reviews). “The authors … present an extremely rich collection of inequalities in a remarkably coherent and unified approach. The book is a major work on inequalities, rich in content and original in organization.” (Siam Review). “The appearance of … Inequalities in 1979 had a great impact on the mathematical sciences. By showing how a single concept unified a staggering amount of material from widely diverse disciplines–probability, geometry, statistics, operations research, etc.–this work was a revelation to those of us who had been trying to make sense of his own corner of this material.” (Linear Algebra and its Applications). This greatly expanded new edition includes recent research on stochastic, multivariate and group majorization, Lorenz order, and applications in physics and chemistry, in economics and political science, in matrix inequalities, and in probability and statistics. The reference list has almost doubled.
Note:
Description based upon print version of record
,
Inequalities: Theory of Majorization and Its Applications; Preface and Acknowledgments from the First Edition; History and Preface of the Second Edition; Overview and Roadmap; Contents; Basic Notation and Terminology; Part I: Theory of Majorization; 1 Introduction; 2 Doubly Stochastic Matrices; 3 Schur-Convex Functions; 4 Equivalent Conditions for Majorization; 5 Preservation and Generation of Majorization; 6 Rearrangements and Majorization; Part II: Mathematical Applications; 7 Combinatorial Analysis; 8 Geometric Inequalities; 9 Matrix Theory; 10 Numerical Analysis
,
Part III: Stochastic Applications11 Stochastic Majorizations; 12 Probabilistic, Statistical, and Other Applications; 13 Additional Statistical Applications; Part IV: Generalizations; 14 Orderings Extending Majorization; 15 Multivariate Majorization; Part V: Complementary Topics; 16 Convex Functions and Some Classical Inequalities; 17 Stochastic Ordering; 18 Total Positivity; 19 Matrix Factorizations, Compounds,Direct Products, and M-Matrices; 20 Extremal Representations of Matrix Functions; Biographies; References; Author Index; Subject Index;
Additional Edition:
ISBN 9780387400877
Additional Edition:
Buchausg. u.d.T. Marshall, Albert W. Inequalities New York : Springer, 2011 ISBN 9780387400877
Language:
English
Subjects:
Economics
,
Mathematics
Keywords:
Ungleichung
;
Statistik
;
Konvexität
;
Ungleichung
;
Statistik
;
Ungleichung
;
Konvexität
DOI:
10.1007/978-0-387-68276-1
URL:
Volltext
(lizenzpflichtig)
URL:
Volltext
(lizenzpflichtig)
Author information:
Arnold, Barry C. 1939-
Author information:
Olkin, Ingram 1924-2016
