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研究生: 吳羽倫
Wu, Yu-Lun
論文名稱: 在整數環中關於矩陣乘法的校正演算法
Correcting Matrix Products over the Ring of Integers
指導教授: 王弘倫
Wang, Hung-Lung
口試委員: 王弘倫
Wang, Hung-Lung
韓永楷
Hon, ‪Wing-Kai
蔡孟宗
Tsai, Meng-Tsung
口試日期: 2021/08/13
學位類別: 碩士
Master
系所名稱: 資訊工程學系
Department of Computer Science and Information Engineering
論文出版年: 2022
畢業學年度: 110
語文別: 英文
論文頁數: 30
中文關鍵詞: 矩陣乘法矩陣乘積校正演算法生成元
英文關鍵詞: matrix multiplication, matrix product, correction, group generator
研究方法: 參與觀察法調查研究
DOI URL: http://doi.org/10.6345/NTNU202201312
論文種類: 學術論文
相關次數: 點閱:133下載:21
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  • 給定三個 n × n 的整數矩陣 A, B, 和 C,其中 C 與 A × B 的乘積有最多 k 個
    元素相異。我們研究如何有效率的修正整數矩陣乘積的錯誤,並找到了時間複雜
    度為 O(k^0.5 × n^2) 的決定性演算法。另外,在執行演算法的過程中所須要處理的數
    字最大值為 O(n^2α^2 + nα),其中 α 是 A, B, 和 C 的元素的最大值。

    Given three n × n matrices A, B, and C with C containing at most k entries differ
    from A × B, we investigate how to find the correct matrix products over the ring over
    integers efficiently and provide a deterministic algorithm running in O(k^0.5 × n^2) time. In addition, the values need to manipulate during the algorithm are O(n^2 × α^2 + n^α), where α is the largest value of entries in A, B, and C.

    致謝 i 中文摘要 ii Abstract iii Contents iv Chapter 1 Introduction 1 1.1 Background 1 1.2 Matrix multiplication 2 1.3 Group testing 2 1.4 The structure of the thesis 3 Chapter 2 Related work 4 2.1 Freivalds' Algorithm 4 2.2 Some other randomized algorithms for certifying 5 2.3 The deterministic algorithm using O(n 2 ) time in the BSS model 8 2.4 Correcting matrix products 10 Chapter 3 The correcting algorithms using the property of polynomial 17 3.1 A simple version of correcting algorithm in BSS model 17 3.2 Increase the time complexity to reduce the scale of numbers 19 Chapter 4 Prevent big numbers by using modulo operations 22 Chapter 5 Conclusions and Future work 28 References 29

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