Two unconstrained procedures to ensure that intrabreed and interbreed genetic and environmental covariance estimates for multibreed populations are computed within the permissible ranges were developed. These procedures were called Partial Scoring and Cholesky Maximization. The Partial Scoring procedure uses partial steps to keep estimates of covariance matrices positive definite at each expect...

The radiosity equation has been usedwidely in computer graphics and thermal engineering applications. The equation is simple to formulate but is challenging to solve when the number of Lambertian surfaces associatedwith an application becomes large. In this paper, we present the algorithms to compute the view factors and solve the set of radiosity equations using an out-of-core Cholesky decompo...

We obtain an explicit Iwasawa decomposition of the symplectic matrices, complex or real, in terms of the Cholesky factorization for positive definite n×n matrices. We also provide a MATLAB program to compute the decomposition. 1. Iwasawa decomposition of the symplectic groups Let G be the real (noncompact) symplectic group [3, p.129] (the notation there is Spn), [4, p.265] G := Spn(R) = {g ∈ SL...

We obtain several asymptotic results on the powers of a square matrix associated with SVD, QR decomposition and Cholesky decomposition. 1. Yamamoto’s theorem Given X ∈ Cn×n, the eigenvalue moduli of X are always less than or equal to the spectral norm of X since ‖X‖ := max ‖v‖2=1 ‖Xv‖2 and if Xv = λv for some unit vector v, then |λ| = ‖Xv‖2 ≤ ‖X‖. So for all m ∈ N, r(X) ≤ ‖X‖ ≤ ‖X‖, where r(X) ...

In this paper we propose and study an optimization problem over a matrix group orbit that we call Group Orbit Optimization (GOO). We prove that GOO can be used to induce matrix decomposition techniques such as singular value decomposition (SVD), LU decomposition, QR decomposition, Schur decomposition and Cholesky decomposition, etc. This gives rise to a unified framework for matrix decompositio...

According to the dynamic GPS rapid positioning ambiguity resolution problems, a modified algorithm for rapid integer ambiguity resolution is proposed. Firstly, a method of QR decomposition is applied on the observation matrix to construct the left null space matrix in order to construct the left null space matrix, so as to decrease dimensions of the matrix and to satisfy rapid ambiguity resolut...

In this paper, a matrix-free posterior ensemble Kalman filter implementation based on a modified Cholesky decomposition is proposed. The method works as follows: the precision matrix of the background error distribution is estimated based on a modified Cholesky decomposition. The resulting estimator can be expressed in terms of Cholesky factors which can be updated based on a series of rank-one...

The Cholesky decomposition-block diagonalization (CD-BD) interference alignment (IA) for a multiuser multiple input multiple output (MU-MIMO) relay system is proposed, which designs precoders for the multiple access channel (MAC) by employing the singular value decomposition (SVD) as well as the mean square error (MSE) detector for the broadcast Hermitian channel (BHC) taken advantage of in our...