BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//CS-TR-65-28
       ENTRY:: January 19, 1996
ORGANIZATION:: Stanford University, Department of Computer Science
       TITLE:: Matrix theorems for partial differential and difference
               equations
        TYPE:: Technical Report
      AUTHOR:: Miller, John J. H.
      AUTHOR:: Strang, Gilbert
        DATE:: July 1965
       PAGES:: 36
    ABSTRACT:: We extend the work of Kreiss and Morton to prove: for some
               constant K(m), where m is the order of the matrix A,
               $|A^(n)v| \leq C(v)$ for all n $geq$ 0 and |v| = 1 implies
               that $|{SAS}^{-1}| \leq 1$ for some S with $|S^{-1}| \leq 1$,
               |Sv| $\leq$ k(m)C(v). We establish the analogue for
               exponentials $e^{Pt}$, and use it to construct the minimal
               Hilbert norm dominating $L_2$ in which a given partial
               differential equation with constant coefficients is
               well-posed.
       NOTES:: [Adminitrivia V1/Prg/19960119]
         END:: STAN//CS-TR-65-28