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

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/74950

Title:	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
Authors:	徐一民;Hsu, Yi-Min
Contributors:	數學系
Keywords:	有效電組;網格圖;effective resistances;grid
Date:	2017-07-17
Issue Date:	2017-10-27 16:12:49 (UTC+8)
Publisher:	國立中央大學
Abstract:	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.
Appears in Collections:	[Graduate Institute of Mathematics] Electronic Thesis & Dissertation

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