利用路徑積分法求解廣義特徵值問題之數值研究

Abstract

本文係經由研讀了數篇利用路徑積分求解廣義特徵值問題的論文, 並對於其中初始值的選取與調整提出些許改進的方案,另外本文內也附 上了兩個數值實驗,其一是一個淺波方程的有限差分數學模型,另一個 是一個擁有簇聚特徵值的矩陣。

We studied several papers which relative to the eigensolver base on the theory of contour integration and tried to find the most effective scheme by adapting the parameters and deciding to restart or not. Our experimental targets are two different type of matrices. One of them is a finite difference model for the shallow wave equations. The other one is a matrix with cluster spectrum.