P. Benner and R. Byers. An arithmetic for matrix pencils. In A. Beghi, L. Finesso, and G. Picci, editors, Mathematical Theory of Networks and Systems, pages 573--576, Il Poligrafo, Padova, Italy, 1998. 20 Home/Search Document Details and Download
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The Generalized Newton Iteration for the Matrix Sign Function - Sun, Quintana-Orti (1997) (Correct)
....are inverse free iteration schemes for the matrix sign function based on polynomial approximations to the inverse [20] Such schemes, however, have bounded convergence regions. Other inverse free iterative schemes overcome these problems, though at the expense of a much higher computational cost [6,8]. The generalized Newton iteration is attractive in that unlike QZ algorithm [22] the computation of spectral subspaces does not depend on the computation of the eigenvalues and the reordering of the computed eigenvalues, and the algorithmic building blocks are mainly triangular factorizations ....
P. Benner and R. Byers, An arithmetic for matrix pencils, in Proceedings MTNS'98, Padova, Italy, 1998.
Evaluating Products of Matrix Pencils and Collapsing Matrix.. - Benner, Byers (1999) (1 citation) Self-citation (Benner Byers) (Correct)
....and deflating subspaces of the matrix pencil E Gamma A. Although the E k must formally be nonsingular in order for the expression (1) to be welldefined, often the invariant subspace problem can be extended to a generalized deflating subspace problem even for singular matrices E k [3, 4, 10, 16, 20, 28]. Consider, for example, the recurrence relation E k x k 1 = A k x k ; 2) where E k ; A k 2 R n Thetan and x k 2 R n , k = 0, 1, 2, 1. The product (1) is the p step monodromy matrix P satisfying x p = Px 0 exactly when x 0 and x p participate in (2) If some of the E k s are ....
....matrix, but there is still a p step relation between an initial state x 0 and the p step later state x p . The monodromy relation between x 0 and x p remains well defined regardless of whether or not it is a linear transformation. A representation of the monodromy relation is suggested in [3, 4]. To each pair of matrices E; A 2 R n Thetan a linear relation on R n Theta R n (EnA) f(y; x) 2 R n Theta R n j Ey = Axg : is associated. If E is nonsingular, then (EnA) is the linear transformation E Gamma1 A. The recurrence (2) is then fully described by the inclusions (x k 1 ....
P. Benner and R. Byers. An arithmetic for matrix pencils. In A. Beghi, L. Finesso, and G. Picci, editors, Mathematical Theory of Networks and Systems, pages 573--576, Il Poligrafo, Padova, Italy, 1998. 20
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