| 术语 | conjugate direction method |
| 释义 | conjugate direction method 共轭方向法 A method for solving the symmetric positive definite linear equations. It modifies the approximate solution alternately along a set of conjugate directions until the satisfactory solution is obtained. If P&-{1},P&-{2},…,P&-{n} represent the set of conjugate directions,i.e. the set of vectors satisfying the relation(P&-{i},AP&-{j})=0= (i≠j), then the most simple form of the conjugate direction method is (a) find rK+1=b-AxK-1,(b) find μK=(P&-{K},rK-1)／(P&-{K},AP&-{K}),(c) findxK=xK-1 +μ&-{K}P&-{K},K=1,2,….In theory, after n steps of computation according to the above formulas, the accurate solution should be found, so that the con jugate direction method belongs to the class of direct methods. However, because of the round-off errors existing in the computing procedure, the accurate solution can not be obtained in n steps. So generally, this method is treated as aniterative approach until the satisfactory accuracy is found. 求解对称正定线性方程组的一种方法,其特点是沿着一组相互共轭方向轮流对近似解进行修正,直到得出满意解 答为止。如果以P&-{1},P&-{2},…,P&-{n}表示一组共轭方向,即满足关系 (P&-{i},AP&-{j})=0= (i≠j),的一组向量,则共轭方向法的一种最简单的形式为: (1) 求rK-1=b-AxK-1,(2) 求μK=(P&-{K},rK-1)／(P&-{K},AP&-{K}),(3) 求xK=xK-1+μKP&-{K},K=1,2,…。从理论上说,按上式计算n步后应该得 出方程组的精确解,所以共轭方向法属于直接法范围。但由于计算过程中存在舍入误差,即使计算n步也得不到精确解。 所以通常把这一方法当作迭代法来进行,一直计算到满意精度为止。 |
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