[BANANA] Two SCCM seminars next week

[Rasmus Munk Larsen]

Next week we have two SCCM seminars. At our regular Monday seminar,
Anne Greenbaum will be speaking, while next Friday we have a special
seminar with Valeria Simoncini. Also remember that Sabine Van Huffel's
class, CS339: Numerical Methods in Biomathematics, begins on Wednesday
at 3.15 pm. For further information see

  http://www-sccm.stanford.edu/nflash/nf-biomathematics.html.

Best regards,
  Rasmus Munk Larsen

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DATE:    2 October 2000
TIME:    4.15 pm
ROOM:    Biot 185, Herrin Hall
SPEAKER: Anne Greenbaum
FROM:    University of Washington
E-MAIL:  greenbau at math.washington.edu

TITLE: Using the Cauchy Integral Formula and the Partial Fractions 
       Decomposition of the Resolvent to Estimate || f(A) ||

ABSTRACT:
Given an entire analytic function f and certain spectral information
about a matrix A, one often is interested in estimating || f(A) ||,
where || || denotes the spectral norm.  Estimates have
been developed in terms of eigenvalue condition numbers and in
terms of epsilon-pseudospectra, for example.  We extend the
bound based on eigenvalue condition numbers to the nondiagonalizable
case and show that it can be derived from the Cauchy integral formula
by integrating around a union of closed curves, each of which encloses
one eigenvalue, and replacing the norm of the sum of these integrals
by the sum of the norms.  Hence this bound is tighter than any obtained
by replacing the norm of the integral about such curves by the
integral of the norm of the integrand.  We also suggest a more flexible
variant of this bound that allows for a smooth transition between the
diagonalizable and nondiagonalizable cases and gives better estimates
in some instances.


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DATE:    Friday 6 October 2000
TIME:    4.35 pm
ROOM:    Gates B08
SPEAKER: Valeria Simoncini
FROM:    Istituto di Analisi Numerica del CNR, Pavia, Italy
E-MAIL:  val at dragon.ian.pv.cnr.it

TITLE: On the numerical solution of linear systems with a
       quadratic parameter


ABSTRACT:

The solution of the large linear system $(\sigma^2 A + \sigma B + C) x
= b$ with $A, B, C\in {\bf C}^{n\times n}$ large complex symmetric
matrices, $b, x\in {\bf C}^n$ long vectors and $\sigma\in {\bf C}$,
arises in several applications involving the solution of certain
difference and differential equations.

In several cases, the solution need me monitored as the complex
parameter $\sigma$ varies in a wide range of values.  The application
of a sparse direct scheme necessitates one symbolic analysis and as
many practical factorizations as the number of parameter values at
hand, causing a linear computational cost growth with the number of
parameters.

An alternative approach, borrowed from the eigenvalue problem
community, consists of transforming the given problem into the
mathematically equivalent complex linear system $(T+\sigma S) z = d$
of double size.  This system is solved by means of an iterative method
that can handle the occurrence of several simultaneous values of the
parameter, at a cost that grows sub-linearly with the number of
parameter values.  In this talk we shall discuss an ad--hoc
implementation that effectively exploits the symmetry of the original
problem.  Experimental results on real application problems will be
reported.


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See the SCCM homepage for a full list of fall seminars:
http://www-sccm.stanford.edu/nflash/nf-frameset.html