Sentence examples for matrix of the linear from inspiring English sources

Taking advantage of the special block Toeplitz structure of the matrix of the linear system, a fast iterative and preconditioned numerical method yielding large memory savings is proposed.

The appropriate values for the parameters involved in the new preconditioners are estimated, so that the numerical conditioning and the spectral property of the saddle-point matrix of the linear system can be substantially improved.

We show that accuracy of the method for quadratic functions improves with decreasing this parameter, however, at the same time, the condition number of the matrix M, which is the local matrix of the linear system for computing the discrete gradient, increases to infinity when the parameter goes to zero, so one needs to choose a compromise between accuracy and solvability of the local system.

where be a fundamental matrix of the linear equation.

where Φ ( t, t 0 ) is the fundamental matrix of the linear equation x ˙ ( t ) = A ( t ) x ( t ).

v ( t, α ) being the solution of (5.4) and X + ( t, α ) the fundamental matrix of the linear equation x ˙ = f + ′ ( q + ( t, α ) ) x.

The coefficient matrices of the linear systems are structured such that their matrix-vector multiplications can be computed efficiently.

Together with the matrices of the linear part of the localised nonlinearity, the MCDFM forms the so-called harmonic nonlinear super-model (HNSM).

More importantly, the proposed method is robust since the linear system is independent of the derivatives of system matrices and some weight constants are introduced in the coefficient matrices of the linear system to reduce the condition number.

then the matrices of the linear operators,andnd in the pullback bases are.

Before the real-time simulation loop, the element stiffness matrices of the linear elasticity ({mathbf {K}}^e_0) and the reduction lists described in "Efficient matrix/vector assembly in a sparse storage format" are calculated.