| 高阻尼因子对阻尼最小二乘法效果的影响和克服 |
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| 引用本文： | 陈钟琦.高阻尼因子对阻尼最小二乘法效果的影响和克服[J].现代地质,1988(2). |
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| 作者姓名： | 陈钟琦 |
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| 摘 要： | 阻尼最小二乘法(包括改进的阻尼最小二乘法,下同)是目前公认的求解无约束最优化问题最优秀的算法之一,在解决实际问题中发挥了重要作用。但它并不是完美无缺的。本文提出高阻尼因子对阻尼最小二乘法效果的影响就是它们存在的,但尚未引起充分重视的问题。这个问题关系到使阻尼最小二乘法收敛缓慢甚至完全失效。本文提出设立高截止阻尼因子λ_h,并给出它的计算方法。它标志:超过λ_h的一切阻尼因子所相应的阻尼最小二乘法改正向量的步长已小于该点最速下降法的最优步长。这时应采取最速下降法探索极小点才能获得好的效果。通过设立高截止阻尼因子,将阻尼最小二乘法与最速下降法有机地结合起来,从而克服高阻尼因子对阻尼最小二乘法效果所带来的不良影响,也是对阻尼最小二乘法的进一步完善和补充。 实践证明:本文提出的设置高截止阻尼因子的理论推导和计算方法是正确的,效果明显。
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| 关 键 词： | 阻尼最小二乘法 阻尼因子 |
THE INFLUENCE OF THE HIGH DAMPING FACTOR TO THE RESULT OF DAMPED LEAST SQUARE METHOD AND IT'S OVERCOMING |
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| Chen Zhongqi.THE INFLUENCE OF THE HIGH DAMPING FACTOR TO THE RESULT OF DAMPED LEAST SQUARE METHOD AND IT''''S OVERCOMING[J].Geoscience——Journal of Graduate School,China University of Geosciences,1988(2). |
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| Authors: | Chen Zhongqi |
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| Institution: | China University of Geosciences |
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| Abstract: | Damped Least square method (including damped least method improved, the same below) is one of the best algorithm in solving unconstrained optimization nowadays. It plays an important role in solving practical problems, but it is not perfect.
The manifestation of that the result of damped least square method is affected by the high damping factor in this paper, shows that this is an existing problem but which is not noticed fully yet. This problem concerns with the slow converging or perfect fai'ing in damped leas tsquare method. This paper presents the setting of damping factor of high cut off ,ih and provides the computational method about h It proves that the step of corrective vector for all damping factors larger than h in damped least square method had been smaller than the best step in steepest descent method. In such a case we should adopt steepest descent method to find minimum point, so that we can get better result. Through setting damping factor of high cut off h and combining damped Jeast square method with steepest descent method to overcome the bad influence produced by highdamping factor on damped least square method is also a further improve ment and complement to the damped least square method.
The practice proved that theoretical deduction and computation on the setting of damping factor of high cut off are correct, and its effects are apparent. |
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| Keywords: | : damped least square method damping factor |
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