The calculation of the distance to a nearby defective matrix
This work provides a faster computational method for a specific linear algebra problem, but it is incremental as it extends an existing method.
The paper presents a new fast algorithm for computing the distance of a matrix to a nearby defective matrix, formulated as a constrained singularity problem, with numerical results demonstrating its performance.
In this paper a new fast algorithm for the computation of the distance of a matrix to a nearby defective matrix is presented. The problem is formulated following Alam & Bora (Linear Algebra Appl., 396 (2005), pp.~273--301) and reduces to finding when a parameter-dependent matrix is singular subject to a constraint. The solution is achieved by an extension of the Implicit Determinant Method introduced by Spence & Poulton (J. Comput. Phys., 204 (2005), pp.~65--81). Numerical results for several examples illustrate the performance of the algorithm.