A new class of decomposition for symmetric systems (Q1198362)

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.