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- W72191520 abstract "This chapter highlights conjugate gradient-type methods. A large number of iterative methods for solving linear systems of equations can be derived as minimization methods. In the context of minimization, the Gauss–Seidel method is sometimes known as the method of univariate relaxation, because at each iteration, only a single variable is changed. The most efficient way to obtain a set of conjugate direction vectors is to use the conjugate gradient method, which generates the direction vectors in conjunction with carrying out the conjugate direction method. There is a close relationship between the conjugate gradient algorithm and the Lanczos method for computing eigenvalues of a symmetric matrix. There are two standard approaches to reducing the amount of work and storage in the generalized conjugate residual algorithm. The first is called truncation and the second is called restarting. Both truncation and restarting destroy the finite convergence property. One of the most common preconditioners for nonsymmetric matrices is incomplete LU (ILU) factorization, which corresponds to incomplete Cholesky factorization for symmetric matrices." @default.
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- W72191520 date "1993-01-01" @default.
- W72191520 modified "2023-09-25" @default.
- W72191520 title "Conjugate Gradient-Type Methods" @default.
- W72191520 doi "https://doi.org/10.1016/b978-0-12-289253-0.50013-0" @default.
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