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研究生： 徐一民
Yi-Min Hsu
論文名稱： 網格圖上有效電阻計算方法的比較
A comparison of methods to determine effective resistances in a grid
指導教授： 葉鴻國
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系
Department of Mathematics
論文出版年： 2017
畢業學年度： 105
語文別： 英文
論文頁數： 26
中文關鍵詞： 有效電組 、網格圖
外文關鍵詞： effective resistances, grid
相關次數： 點閱：13  下載：0 
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    • 在這份報告中，我們將回顧並比較文獻中已知用來計算網格圖中兩點間電阻的四種方法。
    首先，我們說明如何使用圖的拉普拉斯譜來計算有效電阻。
    其次，我們使用拉普拉斯矩陣的偽逆矩陣來計算有效電阻。
    接著，我們使用電阻間串聯、並聯和 Y-Delta 變換來計算網格圖中兩點間的有效電阻。
    最後，我們將介紹著名的克希荷夫理論和使用這理論來計算電阻網路內兩點之間的有效電阻。

    In this report, we survey four existing methods to
    determine resistance distances between two nodes on a grid.
    First, we show how to compute the effective resistances by using the spectrum of Laplacian L of a graph G. Then, we describe how to compute the effective resistances by using the pseudo inverse L^+ of a Laplacian L. Next, we use the the series, parallel and Y-Delta transformations to compute the effective resistances between two nodes in a grid. At last, we introduce the celebrated Kirchhoff's Theorem and use it to compute the effective resistances in a resistance network.

    Introduction, definitions and notation........1 Method A: Using the spectrum of Laplacian L....4 Method B: Using the pseudoinverse L^+ of a Laplacian L...............6 Method C: Using series, parallel and Y-Delta transformations...................8 Method D: Using Kirchhoff's Theorem.................12

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