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| :: Purpose and Summary |
Iterative methods use successive approximations to obtain more
accurate solutions. This book gives an introduction to iterative
methods and preconditioning for solving discretized elliptic partial
differential equations and optimal control problems governed by the
Laplace equation, for which the use of matrix-free procedures is
crucial. All methods are explained and analyzed starting from the
historical ideas of the inventors, which are often quoted from their
seminal works. Iterative Methods and Preconditioners for Systems of
Linear Equations grew out of a set of lecture notes that were improved
and enriched over time, resulting in a clear focus for the teaching
methodology, which: presents historical background, derives complete
convergence estimates for all methods, illustrates and provides MATLAB
codes for all methods, and studies and tests all preconditioners first
as stationary iterative solvers.
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