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題名 | 利用交換電容類神經網路解答線性系統方程式= |
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作者 | 周義昌; |
期刊 | 電信研究 |
出版日期 | 19920600 |
卷期 | 22:3 1992.06[民81.06] |
頁次 | 頁371-389 |
分類號 | 312.2 |
語文 | chi |
關鍵詞 | 方程式; 交換; 解答; 電容; 線性系統; 類神經網路; |
中文摘要 | 從本篇論文中我們應用類神經網路架構,以非演算(Nonalgorithm)和即時(Real Time)方式迅速解出一般在線性系統中之反矩陣和□=□等重要基本問題。首先我們提出一個單層霍普菲爾(Hopfield)類神經網路,以解決正定(Positive Definite)短陣之□=□和反矩陣問題。從系統能量的觀點,這線性方程可很容易地對映到線性霍菲爾類神經網路,另外,此全部類神經網路的能量E所呈現的是一元二次方面式的上凹函數,因此,此系統可以保證最後穩定的狀態是在能量函數的全體極小值(Global Minimum)。所以,整個網路並不需要再利用模擬退火(Simulated Annealing)的過程,以求得能量函數的最佳狀況。 應用交換電官技術,這些短陣線方面解答器,可以直接使用超大型積體電路結構來實現;而由於交換電容電路之資料取樣(Sampled Data)特性,可以直接使用類比信號運算,而不須再利用類比/數位和數位/類比的轉換電路。由於交換電容處理元件的高效率和單純化,可以比同樣信號處理之數位處理元件,利用較少的面積和較低的功率消耗;此外,交換電官是可程式化的,所以上面所提到的各種線性系統解答哈,可利用VLSI技術,直接在同一晶片上進行各種問題的求解,以獲致更佳的利用度。 上述各種問題,由PSPICE的模擬結果,可了解交換電容類神經網路的實用性。由於模擬結果和真實答案間的最大誤差很小,因此,此新的交換電容類神經網路,可以在即時計算□=□、反矩陣和DHT、DFT、DCT等轉換問題上,擔任一很重要角色。 |
英文摘要 | In this paper, we present a noalgorithmic and real time solver based on neural networks to compute the solutions of matrix inverse and □=□, where A is a general linear matrix. First, we apply an one layer structure of Hopfield neural network to calculate the solutions of positive definite matrix □=□ and matrix inverse problem. From the viewpoint of energy, the linear equations can be easily mapped onto the linear-model Hopfield network. Besides, the energy function E of the neural networks is existed with second order. So that, it can be guaranteed that the final steady stage solutions are located in the global minimum of energy function. As a result, the networks do not need the simulated annealing process in order to find the optimum stage of energy function. By applying the SC (Switched Capacitor) technology, this matrix solver can be directly implemented in the VLSI architectures. The additional advantage from this sample-data circuits is to operate directly an analog signals without A/D and D/A conversion. The efficiency and simplicity also make the SC processor require much less area and dc power than the corresponding digital processors from the same signal processing task. In addition, the programmability on the weighting connection of SC neural networks can provide the opportunity in finding the solutions of the above different problems on the same chip. The final simulation results from PSPICE can show that the availability of SC neural networks for solving the linear equations. The results also show that these solvers are very precise because the maximum error between the true value and simulation results in each element are very small. This is also the main reason why this new SC neural circuits can play an important role in the real time computation of matrix problem of □=□, matrix inverse and transformation problems such as DHT, DFT, DCT. |
本系統之摘要資訊系依該期刊論文摘要之資訊為主。