Improving the solution of the symmetric eigenvalue problem and an extension

✍ Scribed by Victor Pan

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 125 KB
• Volume: 5
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/0893-9659(92)90012-x

✦ Synopsis

Based on a multipoint approximation of polynomial values, we accelerate the bisection and divide-and-conquer algorithms for the symmetric eige~value problem. We also propose a new extension of the bisection algorithm to the unsymmetric eigenvalue problem.

In this paper we first improve the bisection algorithm for the symmetric eigenvalue problem by applying the algorithm of Pan [1], which approximates the values of a polynomial p(z) = ~'~.=opiX i on a set of m real points Xl,... ,xm, Izil _< 0, i = 1,...,m. Then we comment on some further extensions, which may be of independent interest. Specifically, the algorithm of Pan [1] reaches the approximations within the error bound