DIFFEL APPROXIMATION APPLIED TO THE SOLU TION OF CONVOLUTION EQUATIONS, (2006)
Bellman, Richard, Kalaba, Robert, Kotkin, AND Bella
In their work on the construction of mathematical models to aid in the study of physiological proc esses connected with cancer chemotherapy, the authors have encountered convolution equations that...
SIMULATION AND STIMULATION (2006)
The paper is devoted to an analysis of the qualities required for the successful construction of mathematical models of economic, psychological, and military processes, and to a discussion of why the...
INVARIANT IMBEDDING AND TIME-DEPENDENT SCATTERING OF LIGHT IN A ONE-DIMENSIONAL MEDIUM, (2005)
Bellman, Richard, Kalaba, Robert, Ueno, Sueo
By means of the invariant-imbedding technique, the integral equations for the reflection and transmission coefficients of radiation in a one dimensional medium are obtained, allowing for the release...
A NOTE ON NONLINEAR SUMMABILITY TECHNIQUES IN INVARIANT IMBEDDING (2005)
BELLMAN,RICHARD, KALABA,ROBERT
The use of principles of invariance, as in invariant imbedding and dynamic programming, leads characteristically to functional equations of the form fn+1(p) = Tn(fn(g(p))), n = 0,1,2,..., where f0(p)...
TOPOPOPOLOGICAL DYNAMICS; A BOOK REVIEW, (2005)
Gottschalk,Walter Helbig, Hedlund,Gustav Arnold, Bellman,Richard
American Mathematical Society Colloquium Publications, vol. 36, Providence, R. I., 1955.
NONLINEAR EXTRAPOLATION AND TWO-POINT BOUNDARY VALUE PROBLEMS, (2005)
Bellman,Richard, Kagiwada,Harriet, Kalaba,Robert
It is suggested that the convergence properties of the usual Picard successive approximation scheme may be improved through use of nonlinear extrapolation techniques. A numerical example is provided....
ON THE APPROXIMATION OF CURVES BY LINE SEGMENTS USING DYNAMIC PROGRAMMING. II (2005)
The technique of dynamic programming is applied to approximate a given continuous function g(x) by a finite number of line segments over the interval a,b . The problem is to determine the constants a...
BELLMAN,RICHARD, KALABA,ROBERT, KOTKIN,BELLA
The application of the simple yet powerful computational technique of polynomial approximation to problems in dynamic programming is initiated. The theoretical applicability of orthogonal polynomials...
STUDIES ON BOTTLENECK PROBLEMS IN PRODUCTION PROCESSES (2005)
BELLMAN,RICHARD, LEHMAN,R. SHERMAN
Two papers are given, their purpose being to study in detail some representative problems which occur in the study of interindustry processes. The general techniques will be those of the theory of...
ON THE 'BANG-BANG' CONTROL PROBLEM, (2005)
Bellman,Richard, Glicksberg,Irving, Gross,Oliver
Let S be a physical system whose state at any time is described by an n-dimensional vector x(t), where x(t) is determined by a linear differential equation Z = Az, with A a constant matrix....
Bellman,Richard, Lehman,R. Sherman
Previous papers have applied the functional equation approach of dynamic programming to the study of variational problems associated with the Sturm-Liouville equation of second order with real...
DYNAMIC PROGRAMMING AND ILL-CONDITIONED LINEAR SYSTEMS, (2005)
Bellman,Richard, Kalaba,Robert, Lockett,Joanne
Dynamic programming, successive approximations, extrapolation, and smoothing are used to treat ill-conditioned systems. Numerical examples are given. (Author)
ON THE PRINCIPLE OF INVARIANT IMBEDDING AND PROPAGATION THROUGH INHOMOGENEOUS MEDIA, (2005)
Bellman,Richard, Kalaba,Robert
The purpose of the paper is to present a new technique for the study of propagation through inhomogeneous and random media, based upon an invariance principle which is called the 'principle of...
APPLICATIONS OF DYNAMIC PROGRAMMING TO SPACE GUIDANCE, SATELLITES, AND TRAJECTORIES. (2005)
Bellman,Richard, Dreyfus,Stuart, Kalaba,Robert
The feasibility of space travel and man-made satellites has triggered a rash of interest in the determination of optimal trajectories and generally in guidance and control processes. These problems,...
DYNAMIC PROGRAMMING AND THE VARIATION OF GREEN'S FUNCTIONS, (2005)
Bellman,Richard, Osborn,Howard
The functional equation technique of dynamic programming is applied to the study of quadratic functionals whose Euler variational equations are linear self-adjoint partial differential equations of...
STABILITY THEORY AND ADJOINT OPERATORS FOR LINEAR DIFFERENTIAL-DIFFERENCE EQUATIONS, (2005)
This paper extends to linear differential-difference equations a number of results familiar in the stability theory of ordinary linear differential equations. In this theory, one considers a system...
Bellman,Richard, Lehman,Sherman
In this paper it is shown how variational techniques can be applied to deduce properties for complex operators and for operators which are non-symmetric. For complex operators use is made of a...
ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF DIFFERENTIAL-DIFFERENCE EQUATIONS, (2005)
Bellman,Richard, Cooke,Kenneth L.
In this paper, the problem was considered of determining the asymptotic behavior of solutions of linear differentialdifference equations whose coefficients possess asymptotic series. Although the...
ON THE COMPUTATIONAL SOLUTION OF TWO-POINT BOUNDARY-VALUE PROBLEMS, (2005)
Bellman,Richard, Brown,Thomas A.
Two-point boundary-value problems for secondorder systems of linear differential equations are usually solved by a process involving the inversion of a certain matrix. If the system is too large, it...
ON THE CONSTRUCTION OF A SIMULATION OF THE INITIAL PSYCHIATRIC INTERVIEW, (2005)
Bellman,Richard, Friend,M. B., Kurland,Leonard
The construction of a simulation of an initial psychiatric interview, which can be regarded as an example of an adaptive, multistage decision process is described in order to augment current methods...
ON COMMUNICATION PROCESSES INVOLVING LEARNING AND RANDOM DURATION, (2005)
Bellman,Richard, Kalaba,Robert
The fundamental problem of determining the utility of a communication channel in conveying information is viewed as a problem within the framework of multistage decision processes of stochastic type,...
ON THE ROLE OF DYNAMIC PROGRAMMING IN STATISTICAL COMMUNICATION THEORY, (2005)
Bellman,Richard, Kalaba,Robert
The object of the paper is to show that the fundamental problem of determining the utility of a communication channel in conveying information can be interpreted as a problem within the framework of...
Bellman,Richard, Brock,Ppaul, Mizuki,Mikiso
Nonlinear dynamics problems prove difficult to investigate analytically or numerically if probabilistic terms are involved in their equations. This paper develops a technique for handling problems of...
ON WEIGHTED PCM AND MEAN SQUARE DEVIATION, (2005)
Bellman,Richard, Kalaba,Robert
Bedrosian has introduced the concept of weighted pulse-code modulation, WPCM. This differs from normal PCM in that the amplitude of the transmitted pulses representing the binary digits in a...
DECISION MAKING IN THE FACE OF UNCERTAINTY: 1 (UNCERTAIN OUTCOME) (2005)
A number of simple multi-stage decision processes where the intuitive concept of maximizing expected gain over expected cost is valid are considered.
DYNAMIC PROGRAMMING, SEQUENTIAL ESTIMATION AND SEQUENTIAL DETECTION PROCESSES, (2005)
Bellman,Richard, Kalaba,Robert, Middleton,David
Some general sequential estimation and sequential detection processes are provided with an analytical formulation through use of the functional equation technique of dynamic programming. Some...
FUNCTIONAL APPROXIMATIONS AND DYNAMIC PROGRAMMING, (2005)
Bellman,Richard, Dreyfus,Stuart
This paper indicates some ways in which the theory of approximation can be used to increase the range of present day computers. Although the primary interest is in applying these techniques to the...
INVARIANT IMBEDDING AND MATHEMATICAL PHYSICS, I: PARTICLE PROCESSES. (2005)
Bellman,Richard, Kalaba,Robert, Wing,G. Milton
Using invariance principles in a systematic fashion, new analytic formulations are derived of the classical particle processes, those of transport theory, radiative transfer; random walk, multiple...
DYNAMIC PROGRAMMINE AND ADAPTIVE PROCESSES--I: MATHEMATICAL FOUNDATION, (2005)
Bellman,Richard, Kalaba,Robert
A foundatio is laid for a mathematical theory of a significant class of decision processes which have not as yet been studied in any generality. These processes, which are described in some detail,...
EFFECTS OF SURFACE TENSION AND VISCOSITY ON TAYLOR INSTABILITY, (2005)
Bellman,Richard, Pennington,Ralph H.
The model used is that of two fluids of infinite depth, with the interface initially in the form of a sine wave with amplitude small compared to wave length. The fluids are considered incompressible,...
AN APPLICATION OF DYNAMIC PROGRAMMING TO THE DETERMINATION OF OPTIMAL SATELLITE TRAJECTORIES, (2005)
Bellman,Richard, Dreyfus,Stuart
Consideration is given to a simplified satellite trajectory problem, corresponding to a flat earth assumption, first treated by Okhotsimskii and Eneev. A numerical solution is presented based upon...
INVARIANT IMBEDDING AND NONVARIATIONAL PRINCIPLES IN ANALYTICAL DYNAMICS, (2005)
Bellman,Richard, Kagiwada,Harriet, Kalaba,Robert
An integration theory is provided for the canonical equations of motion with parallels to the classical theory of Jacobi. The new approach is applicable to the general case where there is no...
A NUMERICAL INVERSION OF THE LAPLACE TRANSFORM, (2005)
Bellman, Richard, Kalaba, Robert, Shiffman, Bernard
Usual analytic methods of inverting the Laplace transformation are mostly impractical for numeri cal work. A method applicable to the numerical analysis of the inverse Laplace transform is dis...
A Numerical Approach to the Convolution Equations of a Mathematical Model of Chemotherapy. (2005)
The new model of drug distribution in the body incorporates the exchange between the stationary and flowing phases in the large blood vessels. This introduces computationally difficult con volution...
A NOTE ON INVARIANT IMBEDDING AND GENERALIZED SEMI-GROUPS, (2005)
Bellman,Richard, Brown,Thomas A.
The use of fixed-point techniques is extended to the solution of certain partial differential equations. These equations have application to problems of neutron transport. (Author)
Bellman,Richard, Elkind,Mortimer, Kotkin,Bella
To study the effect of radiation on the popu lation of cell colonies a simple model is constructed that follows a cell through a two dimensional random walk, where one dimension represents state of...
Toward a generalized theory of uncertainty (GTU)-An outline (2005)
Lotfi A. Zadeh, Richard Bellman, Herbert Robbins
It is a deep-seated tradition in science to view uncertainty as a province of probability theory. The generalized theory of uncertainty (GTU) which is outlined in this paper breaks with this...
Decision Making, Fuzzy Set Theory and Computers. (2002)
Bellman,Richard, Lee,E. Stanley
A summary of the accomplishments of this project is given. A book has been published which contains chapters on can computers think, the digital computers, decision making, puzzles, uncertainty,...
Bellman, Richard, Lehman, Sherman
Legibility of this document is in part unsatisfactory. Reproduction has been made from best available copy. See also AD-606 378.
DYNAMIC PROGRAMMING APPLIED TO CONTROL PROCESSES GOVERNED BY GENERAL FUNCTIONAL EQUATIONS (1998)
BELLMAN,RICHARD, KALABA,ROBERT
The fundu=onal equation technique of dynamic programming is applied to the study of co trol processes governed by equ tions of quite general type. Of particular interest are processes with time lags...
Bellman, Richard, Cooke, Kenneth L.
The theory of invariant imbedding leads to new types of difference approximations to partial differential e ions. To illustrate the type of analysis required to establish the convergence of the...
Recurrence Times for the Ehrenfest Model, (1998)
Bellman,Richard, Harris,Theodore
There is presented a modified scheme of the Ehrenfest model to elucidate certin paradoxes in thermodynamic theory with a continuous time parameter, which was apparently first suggested by A. J. F....
ON GAMES INVOLVING BLUFFING, (1998)
Bellman,Richard, Blackwell,David
A class of two-person games possessing the following general characteristics are considered (a) At the beginning of the game, and at various stages of the game, a chance mechanism furnishes numbers...
STUDIES IN FUNCTIONAL EQUATIONS OCCURRING IN DECISION PROCESSES, (1998)
Harris,T. E., Bellman,Richard, Shapiro,Harold N.
Certain problems are considered which arise from a stody of the Bales decision making model. The Markov process associated with this model is considered and existence and continuity, as well as a...
It is briefly indicated how a technique for the reduction of the solution of differentialdifference equations with one time-lag to the solution of systems of ordinary differential equations can be...
ASYMPTOTIC CONTROL THEORY, (1998)
Some general problems are described concerning the asymptotic behavior of control processes as the time-interval becomes infinite. Some partial results in the general case, and a detailed analysis of...
Bellman, Richard, Kalaba, Robert, Ueno, Sueo
It is shown how the invariant-imbedding technique is used for the derivation of integral equations governing the reflection and the transmission coefficients of radiation in a one-dimensional medium...
INVARIANT IMBEDDING AND A RESOLVENT OF THE PHOTON-DIFFUSION EQUATION, (1998)
Bellman, Richard, Kalaba, Robert, Ueno, Sueo
In the study of radiative transfer, the classical Boltzmann-type approach focuses attention on the statistical behavior of the particles within the medium. There are, however, analytical and...
DYNAMIC PROGRAMMING: A BIBLIOGRAPHY OF THEORY AND APPLICATION, (1998)
Bellman,Richard, Karush,Rebecca
This bibliography is divided into three parts: first, there is a chronological ordering of publications, with authors listed alphabetically under each year; second, an alphabetical index of authors;...
ON THE THEORY OF AGE-DEPENDENT STOCHASTIC BRANCHING PROCESSES, (1998)
Bellman,Richard, Harris,Theodore
The following problem which is of possible biological, chemical and physical interest is investigated. A particle existing at time t sub 1 = 0 is assumed to have probabilities q sub n >or =0, of...
SOME TWO-PERSON GAMES INVOLVING BLUFFING, (1998)
Bellman,Richard, Blackwell,David
A systematic theoretical treatment of a two-person zerosum poker game is presented.
ON SOME VARIATIONAL PROBLEMS OCCURRING IN THE THEORY OF DYNAMIC PROGRAMMING, (1998)
Bellman,Richard, Glicksberg,Irving, Gross,Oliver
This paper presents some results of an investigation of a class of interesting and important variational problems involving the control of a physical system over a time interval. One large category...
THE STABILITY THEORY OF DIFFERENTIALDIFFERENCE EQUATIONS, (1998)
A survey of the stability theory of linear and nonlinear differential-difference equations is given with particular reference to the applications to the problems of automatic control in systems...
A FUNCTIONAL EQUATION IN THE THEORY OF DYNAMIC PROGRAMMING AND ITS GENERALIZATIONS, (1998)
Bellman,Richard, Lehman,Sherman
Various analytic properties of a particular functional equation are studied together with a number of generalizations of discrete and continuous type.
ON THE CONTINUOUS GOLD-MINING EQUATION, (1998)
Bellman,Richard, Lehman,Sherman
Prepared in cooperation with Stanford Univ., Calif.
SOME COMBINATORIAL PROBLEMS ARISING IN THE THEORY OF MULTI-STAGE PROCESSES, (1998)
Using the technique of continuous approximation, approximate solutions to a number of important multistage scheduling problems are determined. In addition, the functional equation approach of the...
ON THE OPTIMAL INVENTORY EQUATION, (1998)
Bellman,Richard, Glicksberg,Irving, Gross,Oliver
A summary is presented of some results recently obtained in connection with the problem of optimal inventory. Solutions are given for the case of proportional costs and arbitrary demand, and for the...
NOTES ON MATRIX THEORY, VI, (1998)
Bellman,Richard, Glicksberg,Irving, Gross,Oliver
An identity in matrix theory is derived which yields a number of interesting inequalities. (Author)
HYDRODYNAMICAL STABILITY AND POINCARELYAPUNOV THEORY-I, (1998)
Bellman,Richard, Wing,G. Milton
The purpose of the paper is to initiate a rigorous theory of hydrodynamical stability. Results were established corresponding to the classical PoincareLyapunov theory for systems of nonlinear...
ON THE PRINCIPLE OF INVARIANT IMBEDDING AND DIFFUSE RELECTION FROM CYLINDRICAL REGIONS, (1998)
Bellman,Richard, Kalaba,Robert
It is shown that the principle of invariant imbedding (introduced in AD-605 023) permits the treatment of problems of radiative transfer from cylindrical and spherical geometries in a unitary fashion.
ON THE PRINCIPLE OF INVARIANT IMBEDDING AND ONE-DIMENSIONAL NEUTRON MULTIPLICATION, (1998)
Bellman,Richard, Kalaba,Robert, Wing,G. Milton
A new method is introduced for treating problems involving neutron multiplication by fission, with special regard to questions of critical mass and distribution of neutrons. The results dderive from...
Bellman,Richard, Kalaba,Robert, Lockett,Jo Ann
In a recent article, Beck and Rescigno point out that there are some important biochemical and physiological tracer experiments in which it is necessary to determine the weighting function k(t),...
INVARIANT IMBEDDING, PARTICLE INTERACTION AND CONSERVATION RELATIONS, (1998)
Bellman,Richard, Lehman,Sherman
It is shown that for a quite general class of transport processes involving particle-particle interaction, as well as the usual particle-medium interaction, difference approximations can be obtained...
Bellman,Richard, Cherry,I., Wing,G. M.
The purpose of this paper was to introduce a new method for the numerical integration of a class of nonlinear hyperbolic partial differential equations which admit shocks. The equation u sub t = -uu...
Bellman,Richard, Dreyfus,Stuart
The paper is devoted to the computational solution of dynamic programming processes. The functional-equation approach is used to treat a tactical air-warfare model that A. Mengel previously...
Bellman,Richard, Kalaba,Robert, Wing,G. Milton
Consideration is given to a one-dimensional version of the reflection and transmission of neutrons, and the phenomenon of critical mass. Although the effects of fission, capture and forward and...
RANDOM WALK, SCATTERING AND INVARIANT IMBEDDING. I: ONE-DIMENSIONAL DISCRETE CASE, (1998)
Bellman,Richard, Kalaba,Robert
In this paper, a new method was introduced of treating problems involving random walk processes, based upon the principle of invariant imbedding which were introduced and applied in previous papers....
INVARIANT IMBEDDING, WAVE PROPAGATION AND THE WKB APPROXIMATION, (1998)
Bellman,Richard, Kalaba,Robert
In previous papers, some applications of the principle of invariant imbedding to radiative transfer and neutron diffusion processes were presented. This use of invariance principles was stimulated by...
INVARIANT IMBEDDING AND NEUTRON TRANSPORT THEORY. II: FUNCTIONAL EQUATIONS, (1998)
Bellman,Richard, Kalaba,Robert, Wing,G. Milton
Some one-dimensional fission processes are considered with particular regard to questions of critical length and energy dependence of the products of fission. Various interconnections between the...
ON CONVERGENT PERTURBATION EXPANSIONS, (1998)
Bellman,Richard, Fort,Tomlinson
In this paper, consideration is given the SturmLiouville equation and the problem of obtaining power series expansions for the first characteristic value and function.
ON THE APPLICATION OF DYNAMIC PROGRAMMING TO A CLASS OF IMPLICIT VARIATIONAL PROBLEMS, (1998)
Bellman,Richard, Richardson,John M.
Legibility of this document is in part unsatisfactory. Reproduction has been made from best available copy.
INVARIANT IMBEDDING AND NEUTRON TRANSPORT THEORY - A GENERALIZED APPROACH, (1998)
Bellman,Richard, Kalaba,Robert, Wing,G. Milton
In previous papers the theory of invariant imbedding has been applied to a variety of transport problems. Each problem has been treated individually and any change in the geometry of the medium or...
INVARIANT IMBEDDING AND GENERALIZED TRANSPORT THEORY; A BASIC STOCHASTIC FUNCTIONAL EQUATION, (1998)
Bellman,Richard, Kalaba,Robert, Wing,G. Milton
The aim of the present paper was to extend previous results and techniques so as to include an extensive category of transport processes involving both deterministic and stochastic interaction,...
INVARIANT IMBEDDING AND NEUTRON TRANSPORT THEORY. III. NEUTRON-NEUTRON COLLISION PROCESSES, (1998)
Bellman,Richard, Kalaba,Robert, Wing,G. Milton
The effects on criticality of neutron-neutron collisions involving annihilation are investigated for one-dimensional, single and multi-group cases. The analytic treatment shows that regardless of the...
ON THE K-TH BEST POLICIES, (1998)
Bellman,Richard, Kalaba,Robert
It is shown how the functional equation technique of dynamic programming can be used to determine the optimal, second best, third best, etc., policies for various deterministic and stochastic...
ON THE COMPUTATIONAL SOLUTION OF A CLASS OF FUNCTIONAL DIFFERENTIAL EQUATIONS, (1998)
Functional differential equations of the form (1) u'(t) = g(t,u(t), u(h(t))), and, more generally, of the form (2) u'(t) = g(t,u(t), u(h(u,t))), arise in the construction of realistic models in a...
INVARIANT IMBEDDING AND NEUTRON TRANSPORT THEORY. IV. GENERALIZED TRANSPORT THEORY, (1998)
Bellman,Richard, Kalaba,Robert, Wing,G. Milton
The aim of the paper is to extend previous results and techniques so as to include an extensive category of transport processes involving deterministic and stochastic interactions and general...
INVARIANT IMBEDDING AND WAVE PROPAGATION IN STOCHASTIC MEDIA, (1998)
Bellman,Richard, Kalaba,Robert
The principle of invariant imbedding leads to the formulation of various functional equations describing plane wave propagation in stochastic media. The approach involves first the derivation of...
SEGMENTAL DIFFERENTIAL APPROXIMATION AND THE 'BLACK BOX' PROBLEM, (1998)
Bellman,Richard, Gluss,Brian, Roth,Robert
In previous work on differential approximation, it has been assumed that a black box under consideration may be described by a differential equation of a given type with unknown parameters, which are...
Bellman,Richard, Gluss,Brian, Roth,Robert
It is shown that mathematical techniques of quasilinearization and dynamic programming may be applied to the problem of determining the structure of a system with partially known inputs and partially...
IDENTIFICATION OF DIFFERENTIAL SYSTEMS WITH TIME-VARYING COEFFICIENTS, (1998)
Bellman,Richard, Gluss,Brian, Roth,Robert
Consideration is given to the problem of obtaining an optimal fit to observed data by determining successive approximating systems of linear differential equations with time-varying coefficients....
RELATIVE INVARIANTS AND CLOSURE, (1998)
Bellman,Richard, Richardson,John M.
One of the basic problems of mathematical physics is that of replacing a nonlinear functional equation by a more tractable (analytically and computationally) linear equation. More generally, one...
ADAPTIVE SEGMENTAL DIFFERENTIAL APPROXIMATION, (1998)
An important new method was considered for solving the 'inverse problem' of identifying the nature of black boxes from their outputs. When the box is known to have differential characterizations of...
CHEMOTHERAPY, CONVOLUTION EQUATIONS, AND DIFFERENTIAL APPROXIMATION, (1998)
A review is given of attempts at developing mathematical techniques for use in digital computer programs applicable to a problem of cancer chemotherapy, that of injecting a chemical agent into the...
MATHEMATICAL EXPERIMENTATION IN TIME-LAG MODULATION, (1998)
Bellman,Richard, Buell,June, Kalaba,Robert
Equations of the form du/dt = g(u(t),u(h(t))) arise in a number of scientific contexts. In this paper, we point out some interesting properties of the solution of u'(t) = - u(t - 1 - k sin omega t) +...
INVARIANT IMBEDDING AND NEUTRON TRANSPORT THEORY. V: DIFFUSION AS A LIMITING CASE, (1998)
Bellman,Richard, Kalaba,Robert, Wing,G. Milton
Diffusion theory classically has been regarded as an approximation to the more rigorous (but, of course, not completely rigorous) transport theory under the assumption of high velocity and small mean...
PERTURBATION AND RENORMALIZATION. I, (1998)
Bellman,Richard, Richardson,John M.
The aim of the work is to present a new formalism for obtaining the perturbation solution of a nonlinear equation. The particular equations written will be used to illustrate the technique which is...
DISSIPATION FUNCTIONS AND INVARIANT IMBEDDING, I. (1998)
Bellman,Richard, Kalaba,Robert, Wing,G. Milton
In a series of papers dating from 1956, the authors have used the theory of invariant imbedding to derive a variety of nonlinear functional equations for the description of radiative transfer,...
REDUCTION OF DIMENSIONALITY, DYNAMIC PROGRAMMING, AND CONTROL PROCESSES. (1998)
Bellman,Richard, Kalaba,Robert
A major difficulty in the way of a successful systematic approach to the study of control processes by way of the theory of dynamic programming is the occurrence of processes having state vectors of...
Bellman,Richard, Kalaba,Robert
This Memorandum shows how to approximate a nonlinear partial differential integral equation by a system of ordinary differential equations. A table of necessary constants is provided, and the results...
QUASILINEARIZATION, INVARIANT IMBEDDING, AND THE CALCULATION OF EIGENVALUES, (1998)
Bellman,Richard, Kagiwada,Harriet, Kalaba,Robert
Several eigenvalue problems for systems of ordinary differential equations are considered. They are resolved computationally using the quasilinearization technique, a quadratically convergent...
LINEARIZATION BASED UPON DIFFERENTIAL APPROXIMATION AND GALERKIN'S METHOD. (1998)
Bellman, Richard, Richardson,John M.
A new linearization technique is described, based on differential approximation to ordinary differential equations of deterministic type. Simpler and more flexible than linearization procedures used...
Bellman,Richard, Juncosa,Mario, Kalaba,Robert
Using a generalization of Newton's method, a nonlinear parabolic equation of the form u sub t - u sub xx = g(u), and a nonlinear elliptic equation u sub xx + u sub yy = e superscript u, are solved...
Bellman,Richard, Birkhoff,Garrett, Abu-Shumays,Ibrahim
The volume is a collection of the methods and results of a number of experts in the field of transport theory. There are four main parts: Analytical Neutron Transport; Numerical Neutron Transport;...
On the Maximum Transform and Semigroups of Transformations. (1998)
Bellman, Richard, Karush, William
Part of the Project RAND research program consists of basic supporting studies in mathematics. A problem frequently occurring in applications is that of determining the maximum or minimum value of a...
Simplified analysis of a hyperbolic system (1985)
Bellman, Richard, Meerkov, Semyon M.
The method of generating equation is used in order to reduce a weakly nonlinear hyperbolic system to the standard form, i.e. the form which admits an asymptotic treatment based on the averaging...
The Rayleigh quotient and dynamic programming (1978)
The purpose of this paper is to derive a nonlinear partial differential equation for which λ given by (1.3), is one value of the solution. In Section 2, we derive this equation using a...
The Rayleigh quotient and dynamic programming (1978)
The purpose of this paper is to derive a nonlinear partial differential equation for which λ given by (1.3), is one value of the solution. In Section 2, we derive this equation using a...
Méthodes booléennes en recherche opérationnelle (1970)
HAMMER, Peter L., UDEANU, Sergiu R., BELLMAN, Richard (Préfacier), FOUQUET, Etienne (Traducteur)
371 p., tabl., fig., ref. bib. : 16 p.3/4
Quasilinearization and the estimation of chemical rate constants from raw kinetic data (1967)
Bellman, Richard, Jacquez, J., Kalaba, R., Schwimmer, S.
A technique for estimating chemical rate constants from raw kinetic data is suggested. Such problems are viewed as nonlinear multipoint boundary-value problems for systems of nonlinear ordinary...
ON THE APPLICATION OF DYNAMIC PROGRAMING TO THE DETERMINATION OF OPTIMAL PLAY IN CHESS AND CHECKERS*
INVARIANT IMBEDDING AND THE REDUCTION OF TWO-POINT BOUNDARY VALUE PROBLEMS TO INITIAL VALUE PROBLEMS
ON THE APPLICATION OF DYNAMIC PROGRAMING TO THE DETERMINATION OF OPTIMAL PLAY IN CHESS AND CHECKERS*
INVARIANT IMBEDDING AND THE REDUCTION OF TWO-POINT BOUNDARY VALUE PROBLEMS TO INITIAL VALUE PROBLEMS