## A new class of decomposition for symmetric systems.(English)Zbl 0757.65027

A direct method is described, not based upon Gauss elimination, for decomposing a symmetric matrix $$A$$ into $$L$$, $$D$$, $$L^ T$$ such that the product $$LDL^ T$$ is the inverse of $$A$$. The solution $$X$$ to the system $$AX=B$$ is then computed by three matrix-vector multiplications: $$X=LDL^ TB$$.
This method has two advantages: The decomposed matrices represent the inverse. The decomposition and matrix-vector multiplications can be transferred into a procedure with fewer degree of data dependence which can be used in a parallel environment.

### MSC:

 65F05 Direct numerical methods for linear systems and matrix inversion 65Y05 Parallel numerical computation 15A23 Factorization of matrices
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