A new algorithm for computing the Geronimus transformation with large shifts
The authors consider the numerical computation of the Geronimus transformation with shift and parameter \(C\) of a Jacobi matrix. The numerical behavior of the available algorithms are investigated. The problem of computing the Geronimus transformation is proved to be very ill-conditioned when \(C\) is zero. The authors propose a new algorithm which is more accurate when the shift moves away from the support of the measure and \(C\) is nonzero. The forward errors of the algorithm is estimated and a backward error analysis of the algorithm is presented. Some numerical experiments are shown to illustrate that the method is componentwise forward stable.
scientific article; zbMATH DE number 5709204