Iterative Methods for the Solution of Large Systems of Linear Equations. Additional Methods

Many applications require the solution of very large systems of linear equations Ax = b in which the matrix A is fortunately sparse, i.e., has only relatively few nonzero elements. Such systems arise, for instance, if difference methods or finite element methods arc being used for solving boundary value problems in partial differential equations. The classical elimination methods [see Chapter 4] are not suitable in this context since they tend to lead to the formation of dense intermediate matrices, making the number of arithmetic operations necessary for the solution too large even for present-day computers, not to mention the fact that the memory requirements for such intermediate matrices exceed available space.

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