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.
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