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- W1593622418 abstract "This chapter presents direct methods for solving linear systems. These methods include Gaussian elimination algorithm, Thomas algorithm, LU decomposition, and Cholesky decomposition. For large and/or sparse systems, direct solvers are time-consuming. Iterative solvers are typically used to overcome this problem and might, for a very large number of unknowns, not be applicable at all. Krylov subspace methods form a basis comprised of the sequence of successive matrix powers times an initial residual (the Krylov sequence). The residual is then minimized within this subspace, resulting in an approximation to the solution. Recent developments of solvers rely on algebraic multigrid (AMG) methods that resemble the geometric multigrid (grid-based) process. The conjugate gradient method can be applied for solving a system of linear equations with a symmetric positive definite matrix." @default.
- W1593622418 created "2016-06-24" @default.
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- W1593622418 date "2013-07-26" @default.
- W1593622418 modified "2023-09-25" @default.
- W1593622418 title "Solving Systems of Linear Equations" @default.
- W1593622418 doi "https://doi.org/10.1002/9781119973515.ch8" @default.
- W1593622418 hasPublicationYear "2013" @default.
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