A QR algorithm with variable iteration multiplicity
Each step of an implicit multishift QR algorithm consists of first applying an \(m\times m\) orthogonal transformation, determined by the shifts, which causes a bulge of size \(m\) on the Hessenberg matrix, and then to eliminate that bulge with a sequence of orthogonal transformations. This process may suffer from forward instability and it is discussed how the multiplicity \(m\) should be chosen and the implementation done, to avoid ill effects of this forward instability.
scientific article; zbMATH DE number 1115928
scientific article