Efficient initials for computing maximal eigenpair
For researchers computing eigenpairs of real matrices, this work offers practical initializations that enhance algorithm robustness and speed, though it is an incremental improvement on existing methods.
The paper proposes efficient initial guesses for an inverse iteration algorithm to compute the maximal eigenpair of real matrices, preventing algorithm collapse and improving efficiency. It also extends the approach to the next-to-maximal eigenpair.
This paper introduces some efficient initials for a well-known algorithm (an inverse iteration) for computing the maximal eigenpair of a class of real matrices. The initials not only avoid the collapse of the algorithm but are also unexpectedly efficient. The initials presented here are based on our analytic estimates of the maximal eigenvalue and a mimic of its eigenvector for many years of accumulation in the study of stochastic stability speed. In parallel, the same problem for computing the next to the maximal eigenpair is also studied.