Polynomials and lemniscates of indefiniteness
Research output: Contribution to journal › Article › Scientific › peer-review
|Number of pages||21|
|Publication status||Published - Jun 2016|
|MoE publication type||A1 Journal article-refereed|
For a large indefinite linear system, there exists the option to directly precondition for the normal equations. Matrix nearness problems are formulated to assess the attractiveness of this alternative. Polynomial preconditioning leads to polynomial approximation problems involving lemniscate-like sets, both in the plane and in C-nxn. A natural matrix analytic extension for lemniscates is introduced. Operator theoretically one is concerned with polynomial unitarity and associated factorizations for the inverse. For the speed of convergence and lemniscate asymptotics, the notion of quasilemniscate arises. In the L-2-norm algorithms for solving the problem are devised.
- POTENTIAL-THEORY, NORMAL OPERATORS, APPROXIMATION, ITERATIONS, LENGTH