% formatted on 970304 by morris
\documentstyle{article}
\setcounter{page}{6}
\textheight 9.5in
\textwidth 5.75in
\voffset -1in
\hoffset -0.55in
%\documentstyle{llncs}
\begin{document}
\title{ON INHOMOGENEOUS EIGENPROBLEMS and PSEUDOSPECTRA of MATRICES}
\author{DA YONG CAI \\
Dept. of App. Math., Tsinghua University \\ (Beijing 100084)
P.R. China}
\date{}
\maketitle
    The inhomogeneous eigenvalue(s) of matrices is the complex 
 parameter(s) $c$ with which the equation 
 \[
                 Ax-cx=b
 \]
 has solutions with $\| x \| =1$.
    Where $A$ is a $n \times n$ matrix. $b$ is a nonzero vector. The norm of a
 vector is 2-norm. This problem is resulted from many practical
 applications. It is also of theoritical interests. 

 \vskip 2truemm

     In this paper, the geometry and topology of inhomogeneous
 eigenvalue is considered. a Gerischgorin-like theorem is given.
 Also an iterative algorithm is proposed  of which the convergent
 speed is linear one.

 \vskip 2truemm

    The relationship between inhomogeneous eigenvalues and the  
 psdeudospectra of matrices is explored.The later is getting more
 and more important in numerical linear algebra.

 \vskip 2truemm
    Throughout this paper only real matrices are considered. It is
 easy to generalized our results to complex cases.
\end{document}


