Matrix compensation and diagonal compensation
Let \(A\) be a symmetric positive definite matrix which is decomposed as \(A=B+R\) in some natural way. Typically \(B\) has a special sparsity pattern and \(R\) can be considered as a ``rest''. A matrix \(D\) is called a compensative matrix of \(R\) if \(D-R\) is positive semidefinite. Now define \(M=B+D\), so \(M\) is a compensative matrix of \(A\). \(M\) can be an efficient preconditioner of \(A\). In the paper diagonal compensation is generalized to positive definite matrices. The aim is to preserve the positivity of matrices. Several results are proved on the condition of the preconditioned matrices but no numerical examples are given.
scientific article; zbMATH DE number 903503