Sparse Cholesky factorization of a matrix of type ComplexSparseMatrix
.
For a list of all members of this type, see ComplexSparseCholesky Members.
System.Object
Imsl.Math.ComplexSparseCholesky
Public static (Shared in Visual Basic) members of this type are safe for multithreaded operations. Instance members are not guaranteed to be thread-safe.
Class ComplexSparseCholesky
computes the Cholesky factorization of a sparse Hermitian positive definite matrix A. This factorization can then be used to compute the solution of the linear system .
Typically, the solution of a large sparse positive definite system is done in four steps.
Class ComplexSparseCholesky
realizes all four steps by algorithms described in George and Liu (1981). Especially, step one, is a realization of a minimum degree ordering algorithm. The numerical factorization in its standard form is based on a sparse compressed storage scheme. Alternatively, a multifrontal method can be used. The multifrontal method requires more storage but will be faster than the standard method in certain cases. The multifrontal method is based on the routines in Liu (1987). For a detailed description of this method, see Liu (1990), also Duff and Reid(1983, 1984), Ashcraft (1987) et al. (1987), and Liu (1986, 1989, 1992). The numerical factorization method can be specified by using the
NumericFactorizationMethod property.
The Solve method will compute the symbolic and numeric factorizations if they have not already been computed or supplied by the user through the FactorSymbolically, FactorNumerically,
SetNumericFactor, or
SetSymbolicFactor methods. These factorizations are retained for later use by the Solve
method when different right-hand sides are to be solved.
There is a special situation where computations can be simplified.If an application generates different sparse Hermitian positive definite coefficient matrices that all have the same sparsity pattern, then by using methods GetSymbolicFactor and SetSymbolicFactor the symbolic factorization needs only be computed once.
Namespace: Imsl.Math
Assembly: ImslCS (in ImslCS.dll)
ComplexSparseCholesky Members | Imsl.Math Namespace | Example