Sentence examples for matrix equation by from inspiring English sources

A specially devised preconditioning matrix is used to accelerate the convergence rate of the matrix equation by obtaining the minimized condition number of the influence coefficient matrix.

Therefore, we seek a solution of the matrix equation by using the following iteration formula: u n = α n + 1 u n + 1 + β n + 1 u n + 2 + γ n + 1, n = M − 2, …, 2, 1, 0, (119).

Next, the partial differential equation of motion for the forced vibration of the tower, contacting water (or "wet" tower), subjected to support excitation is transformed into a matrix equation by using the last natural frequencies and normal modes shape of the freely vibrating dry tower.

It is also shown that the conditions are constructive and can be reduced to an algebraic Lyapunov matrix equation by which nonlinear feedback in the observer and its corresponding Lyapunov function can be searched in a way parallel to those of nonlinear control design.

For example, in [2], Nikolaos established some inequalities involving convolution product of matrices and presented a new method to obtain closed form solutions of transition probabilities and dependability measures and then solved the renewal matrix equation by using the convolution product of matrices.

The non-linear differential equations are cast into matrix equations by applying the Bubnov Galerkin weighted residual method, allowing for the solution of the differential equations numerically.

It is based on the assumed mode method, where natural frequencies and modes are determined by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange's equations of motion.

Natural frequencies and modes are determined by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange's equations of motion, where Mindlin theory is applied for plate and Timoshenko beam theory for stiffeners.

In the proposed methodology, a matrix equation is formulated by utilizing the power flow coupling relationships at the interface of the domains.

A complete, general and explicit solution to the generalized Sylvester matrix equation AX − XF = BY, with the matrix F in a companion form, is proposed.

The main constraint is imposed by the steady-state assumption, represented by the matrix equation: S · v = 0 where S is the stoichiometric matrix of the metabolic network and ν the vector of reaction fluxes.