What is such an equation called? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T05:59:04Z http://mathoverflow.net/feeds/question/118046 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/118046/what-is-such-an-equation-called What is such an equation called? Felix Goldberg 2013-01-04T12:11:30Z 2013-01-04T16:36:23Z <p>Is there a name and common technique for such equations, where $A$ and $B$ are matrices and $x$ a vector?</p> <p>$Ax+f(\lambda)Bx=g(\lambda)x$.</p> http://mathoverflow.net/questions/118046/what-is-such-an-equation-called/118066#118066 Answer by S. Sra for What is such an equation called? S. Sra 2013-01-04T16:36:23Z 2013-01-04T16:36:23Z <p>Akin to my comment, this equation can be called a nonlinear <strong>generalized</strong> eigenvalue problem. Usually, $f$ and $g$ are polynomials in $\lambda$, but more general nonlinearities might be allowed. In general, I doubt there will be robust, globally convergent method for this equation that gets all the solutions. The <a href="http://www.maths.dur.ac.uk/events/Meetings/LMS/2008/CLAPDE/Talks/mehrmann1.pdf" rel="nofollow">talk</a> or <a href="http://issnla2010.ba.cnr.it/MehV04.pdf" rel="nofollow">this paper</a> might be good starting points (see especially the paper).</p>