In longitudinal studies, serial dependence of repeated outcomes must be taken into account to make correct inferences on covariate effects. As such, care must be taken in modeling the covariance matrix. However, estimation of the covariance matrix is challenging because there are many parameters in the matrix and the estimated covariance matrix should be positive definite. To overcomes these li...

This paper presents a suucient condition on sparsity patterns for the existence of the incomplete Cholesky factorization. Given the sparsity pattern P(A) of a matrix A, and a target sparsity pattern P satisfying the condition, incomplete Cholesky factorization successfully completes for all symmetric positive deenite matrices with the same pattern P(A). This condition is also necessary in the s...

The Finite Element modelling of geological faults by penalty contact elements may give rise to illconditioned stiffness matrices with the convergence of iterative solvers accelerated, or even allowed for, by the development and implementation of appropriate preconditioners. The present communication investigates the performance of three different block preconditioners in a realistic geomechanic...

The series representation consisting of eigenfunctions as the orthogonal basis is called the Karhunen–Loeve expansion. This paper demonstrates that the determination of eigensolutions using a wavelet-Galerkin scheme for Karhunen–Loeve expansion is computationally equivalent to using wavelet directly for stochastic expansion and simulating the correlated random coefficients using eigen decomposi...

We consider the problem of writing an arbitrary symmetric matrix as the difference of two positive semidefinite matrices. We start with simple ideas such as eigenvalue decomposition. Then, we develop a simple adaptation of the Cholesky that returns a difference-of-Cholesky representation of indefinite matrices. Heuristics that promote sparsity can be applied directly to this modification.

the length of equal minimal and maximal blocks has eected on logarithm-scale logarithm against sequential function on variance and bias of de-trended uctuation analysis, by using quasi monte carlo(qmc) simulation and cholesky decompositions, minimal block couple and maximal are founded which are minimum the summation of mean error square in horest power.