Several conditions for the existence of positive definite solutions and some iterations to find maximal positive definite solutions for these equations were discussed.
For the GEE method, at most 1 out of 1000 simulated datasets with S-design could not converge to a solution because they either encountered a non-positive definite matrix in the iterations or because there was no variation between the clusters in each arm.
Not definitive, just definite.
Moreover, the feedback controller has a definite structure, thus facilitating the iteration of control modeling and control synthesis to reach a sound design.
By mapping the predictor space into a high dimensional feature space using a positive definite kernel and applying in each iteration a model with the structure of an LS-SVM, a kernel version of MLR is obtained.
The reaction sequence can be, in principle, limitlessly iterated to introduce a definite number of the same or different polymer segments at each stage of the iteration.
A feature of this approach is that the linearised system gives rise to a symmetric and positive-definite linear algebra problem at each Newton iteration.
In this case, since the original A matrix (i.e., the covariance matrix) is symmetric, positive definite, and with distinct eigenvalues, then the iterations converge to a diagonal matrix containing the eigenvalues of A in decreasing order [29].
The Jacobi and Gauss-Seidel methods converge if A is strictly diagonally dominant, and the Gauss-Seidel iteration converges if B is positive definite.
For X1 0) = M1, after 9 iterations, we get the unique positive definite solution X 1 ( 9 ) = 1.
Evidently, each step of the nonlinear MHSS-like iteration alternates between two real symmetric positive definite matrices (alpha I+W) and (alpha I+T).
