TAILIEUCHUNG - Báo cáo sinh học: " Computation of all eigenvalues of matrices used in restricted maximum likelihood estimation of variance"

Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học Journal of Biology đề tài: Computation of all eigenvalues of matrices used in restricted maximum likelihood estimation of variance | Genet Sei Evol 1996 28 51-65 Elsevier INRA 51 Original article Computation of all eigenvalues of matrices used in restricted maximum likelihood estimation of variance components using sparse matrix techniques c Robert V Ducrocq Station de génétique quantitative et appliquée Centre de recherches de Jouy-en-Josas Institut national de la recherche agronomique 78352 Jouy-en-Josas cedex France Received 16 March 1995 accepted 3 October 1995 Summary Restricted maximum likelihood REML estimates of variance components have desirable properties but can be very expensive computationally. Large costs result from the need for the repeated inversion of the large coefficient matrix of the mixed-model equations. This paper presents a method based on the computation of all eigenvalues using the Lanczos method a technique reducing a large sparse symmetric matrix to a tridiagonal form. Dense matrix inversion is not required. It is accurate and not very demanding on storage requirements. The Lanczos method the computation of eigenvalues its application in a genetic context and an example are presented. Lanczos method sparse matrix restricted maximum likelihood eigenvalue Resume Calcul de toutes les valeurs propres des matrices utilisées dans 1 estimation du maximum de vraisemblance restreinte des composantes de variance à 1 aide de techniques applicables aux matrices creuses. Les estimations du maximum de vraisem-blance restreinte REML des composantes de variance ont des propriétés intéressantes mats peuvent être coũteuses en temps de calcul et en besoin de mémoire. Le problème vient de la nécessité d inverser de fagon répétée la matrice des coefficients des equations du modèle mixte. Cet article présente une méthode basée sur le calcul des valeurs propres et sur I utilisation de la methode de Lanczos une technique permettant de réduire une matrice creuse symétrique et de grande taille en une matrice tridiagonale. L inversion de matrices denses n est pas nécessaire. Cette methode .

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