Intrinsically dynamic models (IDMs) depict populations whose cumulative growth rate over a number of intervals is equal to the product of the long term growth rates (that is the dominant roots or dominant eigenvalues) associated with each of those intervals. Here the focus is on the birth trajectory produced by a sequence of population projection (Leslie) matrices. The elements of a Leslie matr...

Univariate polynomial root-finding is a classical subject, still important for modern computing. Frequently one seeks just the real roots of a polynomial with real coefficients. They can be approximated at a low computational cost if the polynomial has no nonreal roots, but typically nonreal roots are much more numerous than the real ones. The subject of devising efficient real root-finders has...

We derive the asymptotic distribution of the eigenvalues of a sample covariance matrix with distinct roots. Our theorem can accommodate the situation in which the population covariance matrix is estimated via its sample analogue as well as the more general case in which it is estimated via a √ N -consistent extremum estimator. The sample roots will have a Normal distribution in ∗Address: 2424 M...

We explore the computation of roots of polynomials via eigenvalue problems. In particular, we look at the case when the leading coeecient is relatively very small. We argue that the companion matrix algorithm (used, for instance, by the Matlab roots function) is inaccurate in this case. The accuracy problem is addressed by using matrix pencils instead. This improvement can be predicted from the...

It is suggested that if Guttman's latent-root-one lower bound estimate for the rank of a correlation matrix is accepted as a psychometric upper bound, following the proofs and arguments of Kaiser and Dickman, then the rank for a sample matrix should be estimated by subtracting out the component in the latent roots which can be attributed to sampling error, and leastsquares "capitalization" on t...

This paper is concernedwith large sample approximations of the LR statistic for testing the hypothesis that the smallest eigenvalues of a covariance matrix are equal. Under a normal population Lawley [1956. Tests of significance for the latent roots of covariance and correlation matrices. Biometrika 43, 128–136.] and Fujikoshi [1977.An asymptotic expansion for the distributions of the latent ro...

The expressive power and intelligence of traditional database systems can be improved by recursion. Using recursion, relational database systems are extended into knowledge-base systems (deductive database systems). Linear recursion is the most frequently found type of recursion in deductive databases. In this paper, an intelligent algorithm to solve the generalized fully instantiated form of t...

The expressive power and intelligence of traditional database systems can be improved by recursion. Using recursion, relational database systems are extended into knowledge-base systems (deductive database systems). Linear recursion is the most frequently found type of recursion in deductive databases. In this paper, an algorithm to solve the generalized partially instantiated form of the same ...

For computing square roots of a nonsingular matrix A, which are functions of A, two well known fast and stable algorithms, which are based on the Schur decomposition of A, were proposed by Björk and Hammarling [3], for square roots of general complex matrices, and by Higham [10], for real square roots of real matrices. In this paper we further consider (the computation of) the square roots of m...

where ε = μq, ε p q = μp. The systems for which small parameter has a fractional power were studied by V.K. Grigorenko in [1]. The case of the simple roots of the characteristic equations and the case of the equation having only one multiple n root were studied separately. Let us construct the asymptotic solution of the system (1) by the method of perturbed characteristic equation [2] for the c...