求符號k階余因式的變形雙圖法
THE MODIFIED DOUBLE-GRAPH METHOD FOR FINDING SYMBOLIC k-ORDER COFACTORS
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摘要: 引入了k階變形雙圖Gij和k階變形矩陣Yij的概念。應(yīng)用它們導(dǎo)出了圖行列式C(Y)和k階余因式Y(jié)(ij)的兩個新表達(dá)式,從而提出了求符號k階余因式Y(jié)(ij)的變形雙圖法。應(yīng)用它可直接且高效地求得Y(ij)的一個多層展開式(沒有專門的符號計算問題),而且不產(chǎn)生對消項(xiàng),所以它優(yōu)于以前的方法。
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關(guān)鍵詞:
- 圖論; 變形雙圖; 圖行列式; 符號k階余因式
Abstract: The concepts of k-order modified double-graphs and k-order modified matrices are introduced. By using them two new expressions of graph determinant C(Y) and k-order cofactor Y(ij)are deduced. Then the modified double-graph method is presented for finding symbolic k-order cofactors. By applying it a multi-layer expansion of Y(ij) can be found directly and efficiently (having no special sign evaluation poblem), and it produces no cancellation terms. Hence it is superior to the previous methods. -
黃汝激,電子科學(xué)學(xué)刊,7(1985)2,81-91.[2]S. J. Mason, Proc. IRE, 41 (1953), 1144-1156.[3]C. L. Coates, IRE Trans. on CT, CT-6(1959), 170-187.[4]W.Mayeda, Graph Theory, John Wiley and Sons, Inc.,(1972).[5]黃汝激,電子科學(xué)學(xué)刊, 7(1985)4,254-266.[6]黃汝激,電子科學(xué)學(xué)刊,8(1986)5,335-342.[7]黃汝激,北京科技大學(xué)學(xué)報,12(1990)4,356-362. -
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