求解線性方程組的迭代法的統(tǒng)一二維迭代法
A UNIFIED APPROACH FOR SOL VING LINE AR EQUATIONSTWO-DIMENSIONAL ITERATIVE METHOD
-
摘要: 求解線性方程組Ax=b的迭代法有其獨(dú)特的實(shí)用意義,但由于其收斂的問題而受到限制。本文導(dǎo)出了常用的雅各比法、高斯-塞德爾法和逐次超松弛法等的統(tǒng)一方法,稱之為二維迭代法,并由此得到了從新的角度改進(jìn)迭代法的收斂性和收斂速度的途徑。理論分析和數(shù)值計(jì)算都表明該方法優(yōu)于常用的迭代法。此方法在解大規(guī)模電路中有用,例如用于VLSI的模擬。
-
關(guān)鍵詞:
Abstract: In this paper, a unified approach of iterative methods, such as Jacobi method, Gauss-Seidel method, SOR method, etc., for solving linear equations is discussed and studied. For the reason stated in this paper, this approach is called 2-dimensional iterative method. The convergence and the rate of convergence of iteration process are improved by using this new approach. The theoretical analysis and the computing results demonstrate that this approach has many advantages over the generally used iterative methods. it is useful in solving the large scale electric circuits, such as VLSI. -
Д.К. 法捷耶夫,B.H.法捷耶娃著,劉克武等譯,線性代數(shù)計(jì)算方法,上海科技出版社,1965年,第231-291頁.[2]I. S. Duff, Proc. IEEE, 65(1977), 500-35.[3]G. D. Hachtel, A. L. Sangiovanni-Vincentilli, ibid., 69(1981), 1264-80.[4]S. L. Richter and R. A. Decarlo, IEEE Trans. on CAS, CAS-30(1983), 347-52.[5]谷獲隆嗣,通信學(xué)會論文志,J65A(1982), 802.[6]張學(xué)銘等,微分方程穩(wěn)定性理論講義,山東人民出版社,1958年,第54-113頁.[7]韓天敏,應(yīng)用數(shù)學(xué)學(xué)報(bào),1977年,第3期,第28頁.[8]L. W. Nagel, Spice-II, A Computer Program to Simulate Semiconductor Circuits, Memorandum No. ERL, M 520, College of Engineering, University of Calfornia Berkeley, 1975. -
計(jì)量
- 文章訪問數(shù): 2285
- HTML全文瀏覽量: 140
- PDF下載量: 484
- 被引次數(shù): 0
下載:
