This article introduces and constructively illustrates the concept of an adaptive homotopy for solving systems of nonlinear equations. Standard homotopy methods rely on a passive continuation parameter moving from 0 to 1 along the real line and are stymied if the homotopy Jacobian matrix becomes...

A Fortran implementation for the "Flexible Least Squares" (FLS) method for time-varying linear regression (FLS-TVLR) is discussed. The latest Fortran implementation for FLS-TVLR, along with tutorials and research publications, can be accessed here: http://www.econ.iastate.edu/tesfatsi/flshome.htm

This article develops a complete system of ordinary differential equations for tracking a single eigenvalue of a parameterized matrix, together with one of its corresponding right or left eigenvectors, over parameter intervals. The feasibility and accuracy of the method are illustrated by...

The complete system of ordinary differential equations developed by Kalaba and Tesfatsion (1981) for tracking solution branches of parameterized nonlinear systems is tested using several illustrative examples. One example is the standard Ramsey optimal growth model, for which analytical...

This article discusses the use of associative memories for obtaining preliminary parameter estimates for nonlinear systems. Annotated pointers to related work can be accessed at http://www.econ.iastate.edu/tesfatsi/vita.htm#MAM

An exact procedure is developed for sequentially updating the optimal solution for a general discrete-time nonlinear least-squares estimation problem as the process length increases and new observations are obtained. The optimal sequential estimation equations are derived by means of an...

This article appeared in Computer Science in Economics and Management (now Computational Economics). Parameter estimation problems for nonlinear systems are typically formulated as nonlinear optimization problems. For such problems, one has the usual difficulty that standard successive...

This article develops a complete system of ordinary differential equations for tracking the Frobenius-Perron root (largest eigenvalue) of a parameterized matrix, together with a unit-normalized right eigenvector, over parameter intervals. The feasibility and accuracy of the method are...

This study develops a general multicriteria Flexible Least Squares (FLS) framework for the sequential estimation of process states. Three well-known state estimation algorithms (the Viterbi, Larson-Peschon, and Kalman filters) are derived as monocriterion specializations. The FLS framework is...

This article develops a complete system of ordinary differential equations for tracking the eigenvalues and the right and left eigenvectors of nonsymmetric parameterized matrices over parameter intervals. A simpler reduced form of the ODE system is then derived for tracking the eigenvalues and...