Robert Kalaba

DIFFEL APPROXIMATION APPLIED TO THE SOLU TION OF CONVOLUTION EQUATIONS, (2006)

invariant imhedding.

and (2008)

Robert Kalaba, Thomas Plum, Leigh Tesfatsion, R. Kalaba, T. Plum, L. Tesfatsion

In 1983 an algorithm ~ was introduced for the systematic exact evaluation of higher-order partial derivatives d functions of many variables. In 1986 the library was extended to permit the automatic...

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...

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)

NONLINEAR EXTRAPOLATION AND TWO-POINT BOUNDARY VALUE PROBLEMS, (2005)

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)...

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....

DIFFERENTIAL SYSTEMS FOR EIGENVALUES OF FREDHOLM INTEGRAL EQUATIONS, (2005)

Kagiwada,Harriet, Kalaba,Robert, Schumitzky,Alan

The practical computational solution of nonhomogeneous Fredholm integral equations is extended to the eigenvalue problem for homogeneous integral equations. The eigenvalues and eigenfunctions are...

POLYNOMIAL APPROXIMATION. A NEW COMPUTATIONAL TECHNIQUE IN DYNAMIC PROGRAMMING. I. ALLOCATION PROCESSES (2005)

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...

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)

APPLICATIONS OF DYNAMIC PROGRAMMING TO SPACE GUIDANCE, SATELLITES, AND TRAJECTORIES. (2005)

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...

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,...

ON COMMUNICATION PROCESSES INVOLVING LEARNING AND RANDOM DURATION, (2005)

ON THE ROLE OF DYNAMIC PROGRAMMING IN STATISTICAL COMMUNICATION THEORY, (2005)

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 WEIGHTED PCM AND MEAN SQUARE DEVIATION, (2005)

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...

DYNAMIC PROGRAMMING, SEQUENTIAL ESTIMATION AND SEQUENTIAL DETECTION PROCESSES, (2005)

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...

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...

INVARIANT IMBEDDING AND MATHEMATICAL PHYSICS, I: PARTICLE PROCESSES. (2005)

DYNAMIC PROGRAMMINE AND ADAPTIVE PROCESSES--I: MATHEMATICAL FOUNDATION, (2005)

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...

INVARIANT IMBEDDING AND NONVARIATIONAL PRINCIPLES IN ANALYTICAL DYNAMICS, (2005)

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,...

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...

Direct Transformation of Variational Problems into Cauchy Systems. I. Scalar-Quadratic Case. (2002)

Hess,James, Kalaba,Robert

This series of papers addresses three interrelated problems: the solution of a variational minimization problem, the solution of integral equations, and the solution of an initial valued system of...

Direct Transformation of Variational Problems into Cauchy Systems. II. Scalar-Semi-Quadratic Case. (2002)

Hess,James, Kagiwada,Harriet, Kalaba,Robert

This series of papers addresses three interrelated problems: The solution of a variational problem, the solution of integral equations, and the solution of an initial valued system of...

The Equivalence of Team Theory's Integral Equations and a Cauchy System: Sensitivity Analysis of a Variational Problem. (2002)

Akbari,Alireza, Hess,James, Kagiwada,Harriet, Kalaba,Robert

Team decision theory studies the problem of how a group of decision makers should use information to coordinate their actions. Mathematically, the task is to find functions that maximize an objective...

DYNAMIC PROGRAMMING APPLIED TO CONTROL PROCESSES GOVERNED BY GENERAL FUNCTIONAL EQUATIONS (1998)

A NOTE ON HAMILTON'S EQUATIONS AND INVARIANT IMBEDDING (1998)

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...

INVARIANT IMBEDDING AND THE INTERGRATION OF HAMILTON'S EQUATIONS (1998)

AN INVERSE PROBLEM IN DYNAMIC PROGRAMMING AND AUTOMATIC CONTROL (1998)

INVARIANT IMBEDDING AND SCATTERING OF LIGHT IN A ONE-DIMENSIONAL MEDIUM WITH A MOVING BOUNDARY, (1998)

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...

ON THE PRINCIPLE OF INVARIANT IMBEDDING AND DIFFUSE RELECTION FROM CYLINDRICAL REGIONS, (1998)

ON THE PRINCIPLE OF INVARIANT IMBEDDING AND ONE-DIMENSIONAL NEUTRON MULTIPLICATION, (1998)

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.

NUMERICAL SOLUTION OF FUNCTIONAL EQUATIONS BY MEANS OF LAPLACE TRANSFORM. VIII: DETERMINATION OF WEIGHTING FUNCTIONS, (1998)

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),...

ON THE PRINCIPLE OF INVARIANT IMBEDDING AND NEUTRON TRANSPORT THEORY; I: ONE-DIMENSIONAL CASE, (1998)

RANDOM WALK, SCATTERING AND INVARIANT IMBEDDING. I: ONE-DIMENSIONAL DISCRETE CASE, (1998)

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...

INVARIANT IMBEDDING, WAVE PROPAGATION AND THE WKB APPROXIMATION, (1998)

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 AND NEUTRON TRANSPORT THEORY. II: FUNCTIONAL EQUATIONS, (1998)

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 - A GENERALIZED APPROACH, (1998)

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...

INVARIANT IMBEDDING AND GENERALIZED TRANSPORT THEORY; A BASIC STOCHASTIC FUNCTIONAL EQUATION, (1998)

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 NEUTRON TRANSPORT THEORY. III. NEUTRON-NEUTRON COLLISION PROCESSES, (1998)

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,...

ON THE K-TH BEST POLICIES, (1998)

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...

INVARIANT IMBEDDING AND NEUTRON TRANSPORT THEORY. IV. GENERALIZED TRANSPORT THEORY, (1998)

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...

INVARIANT IMBEDDING AND WAVE PROPAGATION IN STOCHASTIC MEDIA, (1998)

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...

MATHEMATICAL EXPERIMENTATION IN TIME-LAG MODULATION, (1998)

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...

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)

DISSIPATION FUNCTIONS AND INVARIANT IMBEDDING, I. (1998)

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...

REDUCTION OF DIMENSIONALITY, DYNAMIC PROGRAMMING, AND CONTROL PROCESSES. (1998)

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,...

ON A NEW APPROACH TO THE NUMERICAL SOLUTION OF A CLASS OF PARTIAL DIFFERENTIAL INTEGRAL EQUATIONS OF TRANSPORT THEORY, (1998)

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...

QUASILINEARIZATION, INVARIANT IMBEDDING, AND THE CALCULATION OF EIGENVALUES, (1998)

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...

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...

MULTIPLE ANISOTROPIC SCATTERING IN SLABS WITH AXIALLY SYMMETRIC FIELDS, (1998)

Kagiwada,Harriet, Kalaba,Robert

The invariant imbedding approach is applied to the problem of diffuse reflection from a slab having a strongly elongated phase function. The diffuse radiation field is assumed to be axially...

VERIFICATION OF AN APPROXIMATE FORMULA FOR MULTIPLE SCATTERING OF SLOW ELECTRONS, (1998)

Kagiwada,Harriet, Kalaba,Robert

Verification of an approximate formula recently proposed by two Russian authors for the multiple scattering of slow electrons in a gas. This study shows how the true solution can be computed...

INITIAL-VALUE METHODS FOR INTEGRAL EQUATIONS ARISING IN THEORIES OF THE SOLAR ATMOSPHERE, (1998)

Kagiwada,Harriet, Kalaba,Robert, Ueno,Sueo

A computationally useful initial-value theory for determining the intensity of radiation emerging normal to the surface of the atmosphere for comparison with observed profiles is discussed. In this...

SOME NUMERICAL EXPERIMENTS USING NEWTON'S METHOD FOR NONLINEAR PARABOLIC AND ELLIPTIC BOUNDARY-VALUE PROBLEMS, (1998)

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...

A Multicriteria Approach to Model Specification and Estimation (1996)

: In decision theory, incommensurabilities among conflicting decision criteria are typically handled by multicriteria optimization methods such as Pareto efficiency and meanvariance analysis. In...

and (1991)

The Flexible Least Squares Approach to Time-Varying Linear Regression (1988)

Abstract. Parameter estimation problems for nonlinear systems are typically formulated as nonlinear optimization problems. For such problems, one has the usual difficulty that standard successive...

Complete comparative static differential equations (1981)

Local and nonlocal comparative static analysis of economic systems (1981)

Key words and phrases: Parameterized system of equations, complete variational equations, qualitative analysis, numerical implementation, economic applications. 1.

Robert Kalaba, Leigh Tesfatsion, Jonelin Wang

A complete differential-equation system has been developed for the local and nonlocal comparative static analysis of general parametrized economic systems ‘k ( r, a) = 0. The differential equations...

A Multicriteria Approach to Model Specification and Estimation

Programme for "Flexible Least Squares for Approximately Linear Systems"

In decision theory, incommensurabilities among conflicting decision criteria are typically handled by multicriteria optimization methods such as Pareto efficiency and mean-variance analysis. In...

Programme to "Nonlocal Automated Comparative Static Analysis"

Fortran code for the programme used for the article by R. Kalaba and Leigh Tesfatsion "Flexible Least Squares for Approximatley Linear Systems", IEEE Transactions on Systems, Man, and Cybernetics,...

ON A NEW APPROACH TO THE NUMERICAL SOLUTION OF A CLASS OF PARTIAL DIFFERENTIAL INTEGRAL EQUATIONS OF TRANSPORT THEORY*

Fortran code for the programme used for the article by Leigh Tesfatsion "Nonlocal Automated Comparative Static Analysis," Computer Science in Economics and Management_ (now Computational Economics),...

ON A NEW APPROACH TO THE COMPUTATIONAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS

Bellman, Richard, Kalaba, Robert, Kotkin, Bella

ORBIT DETERMINATION AS A MULTI-POINT BOUNDARY-VALUE PROBLEM AND QUASILINEARIZATION

Bellman, Richard, Kagiwada, Harriet, Kalaba, Robert

DYNAMIC PROGRAMMING APPLIED TO CONTROL PROCESSES GOVERNED BY GENERAL FUNCTIONAL EQUATIONS*

ON A NEW COMPUTATIONAL SOLUTION OF TIME-DEPENDENT TRANSPORT PROCESSES, I. ONE-DIMENSIONAL CASE

Bellman, Richard, Kalaba, Robert, Prestrud, Marcia

ON THE FUNDAMENTAL EQUATIONS OF INVARIANT IMBEDDING, I

DYNAMIC PROGRAMMING, SEQUENTIAL ESTIMATION AND SEQUENTIAL DETECTION PROCESSES

Bellman, Richard, Kalaba, Robert, Middleton, David

A MATHEMATICAL THEORY OF ADAPTIVE CONTROL PROCESSES

SOME MATHEMATICAL ASPECTS OF OPTIMAL PREDATION IN ECOLOGY AND BOVICULTURE

DISSIPATION FUNCTIONS AND INVARIANT IMBEDDING, I

INVARIANT IMBEDDING, CONSERVATION RELATIONS, AND NONLINEAR EQUATIONS WITH TWO-POINT BOUNDARY VALUES

INVARIANT IMBEDDING AND THE REDUCTION OF TWO-POINT BOUNDARY VALUE PROBLEMS TO INITIAL VALUE PROBLEMS

WAVE BRANCHING PROCESSES AND INVARIANT IMBEDDING, I

INVARIANT IMBEDDING AND NEUTRON TRANSPORT IN A ROD OF CHANGING LENGTH

INVARIANT IMBEDDING, WAVE PROPAGATION, AND THE WKB APPROXIMATION

ON THE PRINCIPLE OF INVARIANT IMBEDDING AND DIFFUSE REFLECTION FROM CYLINDRICAL REGIONS

ON THE PRINCIPLE OF INVARIANT IMBEDDING AND ONE-DIMENSIONAL NEUTRON MULTIPLICATION

DYNAMIC PROGRAMMING AND STATISTICAL COMMUNICATION THEORY

RANDOM WALK, SCATTERING, AND INVARIANT IMBEDDING I. ONE-DIMENSIONAL DISCRETE CASE

ON THE PRINCIPLE OF INVARIANT IMBEDDING AND PROPAGATION THROUGH INHOMOGENEOUS MEDIA

ON A NEW APPROACH TO THE NUMERICAL SOLUTION OF A CLASS OF PARTIAL DIFFERENTIAL INTEGRAL EQUATIONS OF TRANSPORT THEORY*

ON A NEW APPROACH TO THE COMPUTATIONAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS

Bellman, Richard, Kalaba, Robert, Kotkin, Bella

ORBIT DETERMINATION AS A MULTI-POINT BOUNDARY-VALUE PROBLEM AND QUASILINEARIZATION

Bellman, Richard, Kagiwada, Harriet, Kalaba, Robert

DYNAMIC PROGRAMMING APPLIED TO CONTROL PROCESSES GOVERNED BY GENERAL FUNCTIONAL EQUATIONS*

ON A NEW COMPUTATIONAL SOLUTION OF TIME-DEPENDENT TRANSPORT PROCESSES, I. ONE-DIMENSIONAL CASE

Bellman, Richard, Kalaba, Robert, Prestrud, Marcia

ON THE FUNDAMENTAL EQUATIONS OF INVARIANT IMBEDDING, I

DYNAMIC PROGRAMMING, SEQUENTIAL ESTIMATION AND SEQUENTIAL DETECTION PROCESSES

Bellman, Richard, Kalaba, Robert, Middleton, David

A MATHEMATICAL THEORY OF ADAPTIVE CONTROL PROCESSES

SOME MATHEMATICAL ASPECTS OF OPTIMAL PREDATION IN ECOLOGY AND BOVICULTURE

DISSIPATION FUNCTIONS AND INVARIANT IMBEDDING, I

INVARIANT IMBEDDING, CONSERVATION RELATIONS, AND NONLINEAR EQUATIONS WITH TWO-POINT BOUNDARY VALUES

INVARIANT IMBEDDING AND THE REDUCTION OF TWO-POINT BOUNDARY VALUE PROBLEMS TO INITIAL VALUE PROBLEMS

WAVE BRANCHING PROCESSES AND INVARIANT IMBEDDING, I

INVARIANT IMBEDDING AND NEUTRON TRANSPORT IN A ROD OF CHANGING LENGTH

INVARIANT IMBEDDING, WAVE PROPAGATION, AND THE WKB APPROXIMATION

ON THE PRINCIPLE OF INVARIANT IMBEDDING AND DIFFUSE REFLECTION FROM CYLINDRICAL REGIONS

ON THE PRINCIPLE OF INVARIANT IMBEDDING AND ONE-DIMENSIONAL NEUTRON MULTIPLICATION

DYNAMIC PROGRAMMING AND STATISTICAL COMMUNICATION THEORY

RANDOM WALK, SCATTERING, AND INVARIANT IMBEDDING I. ONE-DIMENSIONAL DISCRETE CASE

ON THE PRINCIPLE OF INVARIANT IMBEDDING AND PROPAGATION THROUGH INHOMOGENEOUS MEDIA

The flexible least squares approach to time-varying linear regression

A multicriteria approach to model specification and estimation

A FORTRAN program for time-varying linear regression via flexible least squares

Kalaba, Robert, Rasakhoo, Nima, Tesfatsion, Leigh

Nonlocal sensitivity analysis, automatic derivative evaluation, and sequential nonlinear estimation

Automatic Derivative Evaluation in the Optimization of Nonlinear Models.

Kalaba, Robert, Tishler, Asher

A Multicriteria Approach to Model Specification and Estimation