A generalized eigenvalue algorithm for tridiagonal matrix pencils ispresented. The algorithm appears as the time evolution equation of anonautonomous discrete integrable system associated with a polynomial sequencewhich has some orthogonality on the support set of the zeros of thecharacteristic polynomial for a tridiagonal matrix pencil. The convergence ofthe algorithm is discussed by using the solution to the initial value problemfor the corresponding discrete integrable system.
展开▼