國立高雄大學應用數學系

　　　　　　　     　　　106學年度第2學期碩士學位考試口試時間表

學生姓名：林冠宇(M1054109)

口試時間：107年6月29日（星期五）14：30

口試時點：理學院408室

論文題目：Perron-Frobenius theorem and computation on multidimensional arrays

摘　　要：

The Perron - Frobenius theorem shows some important results on nonnegative irreducible matrices. This theorem has various applications and extensions. In this paper, we focus on the nonnegative irreducible matrices. After constructing a linear homotopy, we analyze the solution curve of the linear homotopy and prove that any nonnegative irreducible matrix has the positive eigenpair. This is the main result of the Perron-Frobenius theorem. The skill of the proof can be extended to prove the Perron-Frobenius theorem on tensors. Furthermore, the numerical results computed by the homotopy continuation method on nonnegative irreducible matrices and tensors are presented.