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- W2476011857 abstract "A number of matrix decompositions were described in section 1.3. These include the LU or Cholesky decomposition as well as the QR factorization. Each of these can be used to solve a linear system Ax=b . If the matrix A is sparse, however, the triangular factors L and U are usually much less sparse; this is similar for the unitary and upper triangular factors Q and R. For large sparse matrices, such as those arising from the discretization of partial differential equations, it is usually impractical to compute and work with these factors.Instead, one might obtain an approximate factorization, say, A ≈ LU, where L and U are sparse lower and upper triangular matrices, respectively. The product M=LU then could be used as a preconditioner in an iterative method for solving Ax=b . In this chapter we discuss a number of such incomplete factorizations." @default.
- W2476011857 created "2016-08-23" @default.
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- W2476011857 date "1997-01-01" @default.
- W2476011857 modified "2023-10-16" @default.
- W2476011857 title "11. Incomplete Decompositions" @default.
- W2476011857 doi "https://doi.org/10.1137/1.9781611970937.ch11" @default.
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