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In contrast to earlier techniques, preconditions determine the actual relevance of a specific timing bound.
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The procedure relies on the optimization of the Rayleigh quotient over a subspace of orthogonal vectors by a conjugate gradient technique effectively preconditioned with the pointwise incomplete Cholesky factorization.
As the matrix system is ill conditioned, the collocation technique is preconditioned by a standard Galerkin finite element method using a 9-nodes Lagrangian element which presents decisive advantages: sparsity, reduced condition number, easy treatment of complicated geometries.
In this paper, by adopting the preconditioning techniques, a modified CQ algorithm is named preconditioning CQ algorithm, and its extensions for solving the ESFP have been presented.
In this section, we discuss block diagonal and block-triangular diagonal preconditioning techniques for the linear system (5) and analyze the eigenvalues and eigenvectors of the preconditioned matrices.
matrix via both classical and preconditioning techniques.
The properties of different preconditioning techniques are investigated and reported.
In this section, we propose several modified CQ algorithms with preconditioning techniques and prove the convergence.
To get fast convergence rate of the iterative methods, preconditioning techniques are often used [8].
To shorten this time, various preconditioning techniques were employed before the carbonation test.
The preconditioning techniques are also useful for several other problems and methods.
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