Author
Robert E. Kalaba
Other affiliations: California State University, RAND Corporation, Kyoto Computer Gakuin
Bio: Robert E. Kalaba is an academic researcher from University of Southern California. The author has contributed to research in topics: Integral equation & Nonlinear system. The author has an hindex of 40, co-authored 323 publications receiving 8601 citations. Previous affiliations of Robert E. Kalaba include California State University & RAND Corporation.
Papers published on a yearly basis
Papers
More filters
Book•
01 Jan 1965
TL;DR: Quasilinearization and nonlinear boundary value problems as discussed by the authors, where the boundary value problem is formulated as a quadratic equation of the value of a boundary value.
Abstract: Quasilinearization and nonlinear boundary-value problems , Quasilinearization and nonlinear boundary-value problems , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی
1,163 citations
Book•
01 Jan 1996TL;DR: In this article, the fundamental equation in generalized coordinates was revisited and connections among different approaches were made among various approaches to matrix algebra, matrix algebra and Lagrangian mechanics, including matrix algebra in general coordinates.
Abstract: Preface 1 Introduction 2 Matrix algebra 3 The fundamental equation 4 Further applications 5 Elements of Lagrangian mechanics 6 The fundamental equation in generalized coordinates 7 Gauss's principle revisited 8 Connections among different approaches References Afterword Index
435 citations
TL;DR: A weighted least-square method is utilized to obtain the weights of belonging of each member to the set, which has the advantage that it involves the solution of a set of simultaneous linear algebraic equations and is thus conceptually easier to understand than the eigenvector method.
Abstract: Saaty has solved a basic problem in fuzzy set theory using an eigenvector method to determine the weights of belonging of each member to the set. In this paper, a weighted least-square method is utilized to obtain the weights. This method has the advantage that it involves the solution of a set of simultaneous linear algebraic equations and is thus conceptually easier to understand than the eigenvector method. Examples are given for estimating the relative wealth of nations and the relative amount of foreign trade of nations. Numerical solutions are obtained using both the eigenvector method and the weighted least-square method, and the results are compared.
423 citations
415 citations
Cited by
More filters
Book•
01 Jan 1988TL;DR: This book provides a clear and simple account of the key ideas and algorithms of reinforcement learning, which ranges from the history of the field's intellectual foundations to the most recent developments and applications.
Abstract: Reinforcement learning, one of the most active research areas in artificial intelligence, is a computational approach to learning whereby an agent tries to maximize the total amount of reward it receives when interacting with a complex, uncertain environment. In Reinforcement Learning, Richard Sutton and Andrew Barto provide a clear and simple account of the key ideas and algorithms of reinforcement learning. Their discussion ranges from the history of the field's intellectual foundations to the most recent developments and applications. The only necessary mathematical background is familiarity with elementary concepts of probability. The book is divided into three parts. Part I defines the reinforcement learning problem in terms of Markov decision processes. Part II provides basic solution methods: dynamic programming, Monte Carlo methods, and temporal-difference learning. Part III presents a unified view of the solution methods and incorporates artificial neural networks, eligibility traces, and planning; the two final chapters present case studies and consider the future of reinforcement learning.
37,989 citations
Book•
01 Apr 1988
TL;DR: In this article, the authors discuss the properties of Vectors and Matrices, the Vec-Operator, the Moore-Penrose Inverse Miscellaneous Matrix Results, and the Linear Regression Model.
Abstract: Preface MATRICES: Basic Properties of Vectors and Matrices Kronecker Products, the Vec-Operator and the Moore- Penrose Inverse Miscellaneous Matrix Results DIFFERENTIALS: THE THEORY: Mathematical Preliminaries Differentials and Differentiability The Second Differential Static Optimization DIFFERENTIALS: THE PRACTICE: Some Important Differentials First- Order Differentials and Jacobian Matrices Second-Order Differentials and Hessian Matrices INEQUALITIES: Inequalities THE LINEAR MODEL: Statistical Preliminaries The Linear Regression Model Further Topics in the Linear Model APPLICATIONS TO MAXIMUM LIKELIHOOD ESTIMATION: Maximum Likelihood Estimation Simultaneous Equations Topics in Psychometrics Subject Index Bibliography.
2,868 citations
TL;DR: In this paper, a review of scattering theory required for analysis of light reflected by planetary atmospheres is presented, which demonstrates the dependence of single-scattered radiation on the physical properties of the scatterers.
Abstract: This paper reviews scattering theory required for analysis of light reflected by planetary atmospheres. Section 1 defines the radiative quantities which are observed. Section 2 demonstrates the dependence of single-scattered radiation on the physical properties of the scatterers. Section 3 describes several methods to compute the effects of multiple scattering on the reflected light.
2,691 citations
2,605 citations