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Average case complexity of linear multivariate problems I. Theory

H Woźniakowski
1992 Journal of Complexity  
We study the average case complexity of linear multivariate problems, that is, the approximation of continuous linear operators on functions of d variables.  ...  Tractability of a linear multivariate problem means that the average case complexity of computing an E-approximation is O((l/~)p) with p independent of d.  ...  Part I deals with the theory of linear multivariate problems. Part II will deal with applications of the theoretical results to concrete linear multivariate problems.  ... 
doi:10.1016/0885-064x(92)90001-r fatcat:cap4dlcbfngktnrgo6hut5vd5i

Multivariate complex B-splines and Dirichlet averages

Peter Massopust, Brigitte Forster
2010 Journal of Approximation Theory  
Based on this generalization several identities of multivariate complex B-splines are presented.  ...  The notion of a complex B-spline is extended to a multivariate setting by means of ridge functions employing the known geometric relationship between ordinary B-splines and multivariate B-splines.  ...  Multivariate complex B-splines In this section, we introduce multivariate complex B-splines using a geometrically inspired definition by means of so-called ridge functions and an identity that is known  ... 
doi:10.1016/j.jat.2009.05.002 fatcat:wf7k5uq5djdzvjdjqlx5dcwu74

Real-Symmetric Extensions of Invertible Tuples of Multivariable Continuous Functions

Raymond Mortini, Rudolf Rupp
2011 Complex Analysis and Operator Theory  
doi:10.1007/s11785-011-0158-x fatcat:7tkfeigecnh77kr7wgr3mtwiba

Estimation of Multivariate Complex Normal Covariance Matrices Under an Invariant Quadratic Loss

Yoshihiko Konno
2010 Communications in Statistics - Theory and Methods  
The problem of estimating multivariate complex normal covariance matrices is considered under an invariant quadratic loss function.  ...  Improved estimators include the best triangular equivariant estimators and complex analogues of estimators for multivariate real normal covariance matrices by Haff [1980, Ann. Statist. 8:586-597].  ...  INTRODUCTION The theory of complex random matrices plays a vital role in multidimensional signal processing algorithms[see Maiward and Kraus (1994) , Tague and Caldwell (1994) , Ratnarajah and Vaillancourt  ... 
doi:10.1080/03610920802265194 fatcat:bktjmfkftzf7hksxuohszc5c4e

Complex zero-free regions at large |q| for multivariate Tutte polynomials (alias Potts-model partition functions) with general complex edge weights

Bill Jackson, Aldo Procacci, Alan D. Sokal
2013 Journal of combinatorial theory. Series B (Print)  
We find zero-free regions in the complex plane at large |q| for the multivariate Tutte polynomial (also known in statistical mechanics as the Potts-model partition function) Z_G(q,w) of a graph G with  ...  general complex edge weights w = w_e.  ...  (7.8) It then follows from the Yang-Lee [36] theory of phase transitions that there will be complex zeros of the partition function arbitrarily close (as G grows) to the phase-transition point (q,  ... 
doi:10.1016/j.jctb.2012.08.002 fatcat:ov6ukn6tmnfq5jmzlorgeywhli

Analysis on network properties of multivariate mixed air traffic management technical support system based on complex network theory

Wu Xi-Ping, Yang Hong-Yu, Han Song-Chen
2016 Wuli xuebao  
Air traffic management technical support system provides communication, navigation and surveillance service for air traffic management system and air traffic controller. The failures of some facilities may lead to large delay, even affect air transportation safety. In order to improve the ability of air traffic management technical support system to respond to emergencies, a network model of air traffic management technical support system is presented. The network model of air traffic
more » ... technical support system is established according to the effective coverage of communication, navigation and surveillance facilities, the position of air traffic management technical support system and air route network. Flexibility, robustness and efficiency are used to measure the network. The measure index of air traffic management technical support system network includes degree, degree distribution, strength, clustering coefficient, network performance, betweenness centrality, average shortest path and diameter. For Beijing, Shanghai, Guangzhou, Kunming, Shenyang and Lanzhou flight information regions, the air traffic management technical support networks are built by using the data of air traffic support facilities, air route, air traffic flow, etc. The average degrees, degree distributions, degree-degree correlations, clustering coefficients, average shortest paths and diameters of these netwoks are comparatively analyzed. The results show that the degrees of most nodes are between two and four. The network has a power law distribution, which is the same as that of air transportation network. The degree-degree correlation of air traffic management technical support system network is not assortative nor disassortative mixing, which has random network characteristics. The clustering coefficients of several air traffic management technical support system networks are between 0.25 and 0.39. The clustering value is lower than that of air transportation network. The shortest paths of air traffic management technical support system networks are between 3.16 and 5.05. The average shortest paths of these networks are all 3.4, which exhibits small world characteristics. Network attack based on degrees of priority and random is conducted to several flight information regions of air traffic management technical support network, showing the network is vulnerable. The network performance decreases quickly after degree priority attack. Some key nodes play an important role in the network. The network survivability can be improved after targeted immunized key nodes. The network performance can be improved by using more satellites based air traffic management technical support system. These rules provide theoretical support for improving and expanding air traffic management technical support system, and have practical significance for reducing the influence of emergency on air traffic management system support ability and ensuring the continuous safety of air traffic.
doi:10.7498/aps.65.140203 fatcat:by7gkzyyhzes3mekam56ecqzly

THE INFORMATION THEORY AND COGNITIVE TECHNOLOGIES IN MODELING COMPLEX MULTIVARIABLE DYNAMIC TECHNICAL SYSTEMS
Теория информации и когнитивные технологии в моделировании сложных многопараметрических динамических технических систем

Y. V. Lutsenko, G. V. Serga
2016 Polythematic Online Scientific Journal of Kuban State Agrarian University  
On the other hand, the phenomenological information model can be sufficient to determine the rational design features and parameters of the modes of operation of complex technical systems.  ...  It is proposed to use a new universal innovative method of artificial intelligence for creating phenomenological models of complex technical systems: automated system-cognitive analysis (ASC-analysis)  ... 
doi:10.21515/1990-4665-121-002 fatcat:dzuwwrsrnngzjo4jhipa4jng7q

Preface: Multivariate algorithms and information-based complexity [chapter]

2020 Multivariate Algorithms and Information-Based Complexity  
The field of information-based complexity (IBC), founded by Traub and Wozniakowski in the 1980s, analyzes the information complexity for multivariate problems and determines how it depends on d and ε.  ...  The authors of this book include several of the invited speakers in the workshop Multivariate Algorithms and Information-Based Complexity, which was part of the RICAM Special Semester on Multivariate Algorithms  ...  VI | Preface: Multivariate algorithms and information-based complexity namely the quality of random information in approximation and integration problems.  ... 
doi:10.1515/9783110635461-201 fatcat:tv4wjvc4tfbfppffzld4re33iu

Page 14 of Contemporary Psychology Vol. 21, Issue 1 [page]

1976 Contemporary Psychology  
The book is more success- ful in the first respect than in the second, Multivariate theories have a breadth lacking in univariate theories.  ...  And, are multivariate theory and re- search useful in studying a wide range of behaviors?  ... 

Page 2335 of Mathematical Reviews Vol. , Issue 81F [page]

1981 Mathematical Reviews  
P. 81f:62091 Locally most powerful and other tests for independence in multivariate populations. Analytic function methods in probability theory (Proc. Colloq.  ...  Methods of Complex Anal. in the Theory of Probab. and Statist., Kossuth L. Univ. Debrecen, Debrecen, 1977), pp. 99-121, Colloq. Math. Soc. Janos Bolyai, 21, North-Holland, Amsterdam, 1979.  ... 

Page 148 of Mathematical Reviews Vol. 33, Issue 1 [page]

1967 Mathematical Reviews  
A complex multivariate linear regression theory, based on the complex multivariate Gaussian distribution considered by Goodman [same Ann. 34 (1963), 152-177; MR 26 #3148], is developed, leading to results  ...  P. 822 Some extensions of the Wishart and multivariate t-distributions in the complex case. J. Indian Statist. Assoc. 2 (1964), 131-136.  ... 

Linear Model Theory: Univariate, Multivariate, and Mixed Models

Xianggui Qu
2007 Technometrics  
Most books on the subject have historically discussed univariate, multivariate, and mixed linear models separately, whereas Linear Model Theory: Univariate, Multivariate, and Mixed Models presents a unified  ...  Linear Model Theory: Univariate, Multivariate, and Mixed Models begins with six chapters devoted to providing brief and clear mathematical statements of models, procedures, and notation.  ...  Models with complex predictors, complex responses, or both, motivate the presentation. Contents: Preface. PART I: MODELS AND EXAMPLES. Exercises. 14.  ... 
doi:10.1198/tech.2007.s478 fatcat:2pnzemta5bc3bgpqhbihxthq4i

Page 981 of Mathematical Reviews Vol. , Issue 85c [page]

1985 Mathematical Reviews  
ISBN 0-8218-5006-7 This book contains a very comprehensive treatment of most of the author’s original results in the theory of complex integral rep- resentation of cardinal spline functions.  ...  arising in approxi- mation theory.  ... 

A 'Univariate' Symposium on Multivariate Psychology

ROBERT J. STERNBERG
1976 Contemporary Psychology  
The book is more success- ful in the first respect than in the second, Multivariate theories have a breadth lacking in univariate theories.  ...  And, are multivariate theory and re- search useful in studying a wide range of behaviors?  ... 
doi:10.1037/014831 fatcat:jfxxvzgbkzcb5cwhaw4cvv7cli

Page 2304 of Mathematical Reviews Vol. 58, Issue 3 [page]

1979 Mathematical Reviews  
Rosenbrock [State-space and multivariable theory, Wiley, New York, 1970; MR 48 #3550] is equivalent to defining the set of zeros of G(s) as the set {t,} of complex numbers ¢, for which rank N(t;)< p(N(  ...  Kaczorek (Warsaw) Vandewalle, Joos; Dewilde, P. 58 #15395 A local I/O structure theory for multivariable systems and its application to minimal cascade realization. IEEE Trans.  ... 
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