Sentence examples for matrix analytic solution from inspiring English sources

Wang and Yang (2009) presented a matrix analytic solution for developing the steady-state solution of a control F-policy M/G/1/K model with exponential start-up time.

For the simulation of the gas delivering and the gas taking up cylinder, the proposed solution for the Riccati equation is used; the series expansion (25) and the analytic solution for the matrix exponential (29).

For each channel H v, a numerical search over all angles ψ i ∈ 0,Π) in order to maximize the minimum distance shows us which difference vectors providing the distance d min. And finally, the analytic solution of the matrix Σ can be derived by equalizing the difference distances given by these vectors.

Then the following block matrix lemma is utilized to derive the analytic solution.

Matrix analytic method is used to find an algorithmic solution to the problem.

The above minimization problem has analytic solution in terms of the singular value decomposition (SVD) of the data matrix M. Let M = UΣ V T ∈ R m × n be the SVD of M and partition U, Σ = :diag σ1, σ2, σ3,…, σ400), and N as follows: (5) U : U 1 U 2, Σ = : Σ 1 0 0 Σ 2, V = : V 1 V 2, where Σ1 is a r × r matrix, U1 is m × r, and V1 is n × r.

We impose the approximate analytic solution for the system.

The analytic solution is validated by the finite element analysis.

The dissipative one is cheaply solved by its analytic solution.

An analytic solution is obtained without performing integral transforms.

Two levels of performance evaluation indices are formulated using the matrix analytic techniques.