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Computation of all eigenvalues of matrices used in restricted maximum likelihood estimation of variance components using sparse matrix techniques

Abstract : 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.
Mots-clés : GENETIQUE ANIMALE
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  • HAL Id : hal-02685012, version 1
  • PRODINRA : 122118

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Christèle Robert-Granié, Vincent Ducrocq. Computation of all eigenvalues of matrices used in restricted maximum likelihood estimation of variance components using sparse matrix techniques. Genetics Selection Evolution, BioMed Central, 1996, 28 (1), pp.51-65. ⟨hal-02685012⟩

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