The Charming Leading Eigenpair
For researchers in matrix computation and stability analysis, this work offers an improved initialization for a known algorithm, but the contribution is incremental.
The paper presents an efficient initial value for computing the leading eigenpair of matrices, derived from theoretical estimates of leading eigenvalues. It provides unified estimates for the leading eigenvalue and discusses applications to stability analysis.
The leading eigenpair (the couple of eigenvalue and its eigenvector) or the first nontrivial one has different names in different contexts. It is the maximal one in the matrix theory. The talk starts from our new results on computing the maximal eigenpair of matrices. For the unexpected results, our contribution is the efficient initial value for a known algorithm. The initial value comes from our recent theoretic study on the estimation of the leading eigenvalues. To which we have luckily obtained unified estimates which consist of the second part of the talk. In the third part of the talk, the original motivation of the study along this direction is explained in terms of a specific model. The paper is concluded by a brief overview of our study on the leading eigenvalue, or more generally on the speed of various stabilities.