Relaxation methods for non-Hermitian linear systems
Many iterative methods for the solution of systems of linear equations \(Ax=b\) arise from a splitting \(A=M-N.\) The authors propose two new possibilities. The basic theorem is the following lemma: If \(I-\omega M_ B\) is nonsingular and if t is an eigenvalue of \((I-\omega M_ B)^{-1}((1-\omega)I+\omega N)\) with eigenvector v, normalized by \(v^*v=1,\) then \(t=((1-\omega)+\omega \eta)/(1-\omega m),\) where \(\eta =v^*Nv,\quad m=v^*M_ Bv.\) The authors study how this lemma can be used to describe regions in the complex plane which contain the spectrum of the corresponding iteration operators.
scientific article; zbMATH DE number 4126575
scientific article