A partial pivoting Schur-type algorithm for the factorization of matrices with the Jordan displacement structure

We present a partial pivoting Schur-type algorithm for the factorization of matrices with the Jordan displacement structure. It is shown that a matrix with Jordan displacement structure can be transformed into a Cauchy-like matrix via a matrix with the circulant displacement structure. Using the property that a Cauchy-like matrix retains its displacement structure even though it is pivoted. We present a partial pivoting Schur-like algorithm which is fast and stable for a degenerated or irregular case