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.


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