In general, the coefficient estimates of linear models are carried out using ordinary least squares (OLS) method. Since analysis variance is also a model, coefficients can be estimated least-squares this study, in two-way were performed by Cholesky decomposition. The purpose decomposition finding make variables used model being orthogonal such that important easily identified. sum (row, column,...

This research covers the Intel Direct Sparse Solver for Clusters, the software that implements a direct method for solving the Ax = b equation with sparse symmetric matrix A on a cluster. This method, researched by Intel, is based on Cholesky decomposition and could be considered as extension of functionality PARDISO from Intel MKL. To achieve an efficient work balance on a large number of proc...

We propose a double-robust procedure for modeling the correlation matrix of a longitudinal dataset. It is based on an alternative Cholesky decomposition of the form Σ = DLL>D where D is a diagonal matrix proportional to the square roots of the diagonal entries of Σ and L is a unit lower-triangular matrix determining solely the correlation matrix. The first robustness is with respect to model mi...

Numerical algorithms have two kinds of costs: arithmetic and communication, by which we mean either moving data between levels of a memory hierarchy (in the sequential case) or over a network connecting processors (in the parallel case). Communication costs often dominate arithmetic costs, so it is of interest to design algorithms minimizing communication. In this paper we first extend known lo...

The particular symmetry of the random-phase-approximation (RPA) matrix has been utilized in the past to reduce the RPA eigenvalue problem into a symmetric-matrix problem of half the dimension. The condition of positive definiteness of at least one of the matrices A ± B has been imposed (where A and B are the submatrices of the RPA matrix) so that, e.g., its square root can be found by Cholesky ...

The classical method for estimating the spectral density of a multivariate time series is to first calculate the periodogram, and then smooth it to obtain a consistent estimator. Typically, to ensure the estimate is positive definite, all the elements of the periodogram are smoothed the same way. There are, however, many situations for which different components of the spectral matrix have diff...

The Cholesky decomposition is one of the most efficient preconditioners to iterative schemes for solving linear systems such as the conjugate gradient method. However, we are often faced with situations where a linear system exceeds the capacity of existing memory. In this paper we present an efficient out-of-core implementation of the block Cholesky decomposition on a multi-GPU system, which w...

Generalized linear mixed models(GLMMs) are frequently used for the analysis of longitudinal categorical data when the subject-specific effects is of interest. In GLMMs, the structure of the random effects covariance matrix is important for the estimation of fixed effects and to explain subject and time variations. The estimation of the matrix is not simple because of the high dimension and the ...