[1]智东杰,智慧来.矩阵的Doolittle递归分解算法及符号程序设计[J].智能系统学报,2007,2(1):90-93.
ZHI Dong-jie,ZHI Hui-lai.Recursive algorithm and symbolic programming for matrix Doolittle’s factorization[J].CAAI Transactions on Intelligent Systems,2007,2(1):90-93.
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ZHI Dong-jie,ZHI Hui-lai.Recursive algorithm and symbolic programming for matrix Doolittle’s factorization[J].CAAI Transactions on Intelligent Systems,2007,2(1):90-93.
矩阵的Doolittle递归分解算法及符号程序设计
《智能系统学报》[ISSN 1673-4785/CN 23-1538/TP] 卷:
2
期数:
2007年第1期
页码:
90-93
栏目:
学术论文—人工智能基础
出版日期:
2007-02-25
- Title:
- Recursive algorithm and symbolic programming for matrix Doolittle’s factorization
- 文章编号:
- 1673-4785(2007)01-0090-04
- 关键词:
- 矩阵; Doolittle分解; 算法
- Keywords:
- matrix; Doolittle’s factorization; algorithm
- 分类号:
- TP311.1
- 文献标志码:
- A
- 摘要:
- 将矩阵An×n的Doolittl e分解推广到Am×n上，并在常规的迭代算法上加以创新，给出了递归的分解算法 .在实现算法的过程中，对数据进行了巧妙处理，使中间数据及最终计算结果都具有分数形式，提高了结果的精确度，而且更符合人们阅读的习惯.经过运行测试，算法设计合理，程序运行高效准确.程序是对MathSoft公司的交互式的数学文字软件Mathcad的矩阵分解的数值计算扩充到符号运算.
- Abstract:
-
Apply Doolittle’s factorization of matrix 〖WTHX〗An×n to matrix
Am×nthat h as m rows and n columns, and conceive a new recursive algorithm of Dooli ttle’s factorization of matrix on the basis of traditional iterative algorithm. In the realization of algorithm, the data is skillfully dealt, so the interim data and the result have the form of fraction. These merits improve the result’s exactness. And above that it conforms to readers’ reading habit comp ared to double or float forms. After running it, the result proves that the algo rithm is reasonably designed and the program is running with high proficiency an d exactness. The program is an augmentation of matrix factorization in the MathS oft’s interactive mathematic language software, which promotes matrix factoriza tion from numerical computation to symbolic computation.
- 参考文献/References:
-
［1］陈建平,JERZY W. Cholesky分解递归算法与改进［J］. 计算机研究与发展，2001，38（8 ）：923-926.
?CHEN Jianping, JERZY W. Recursive algorithm and improvement for cholesky factor ization ［J］. Journal of Computer Research and Development, 2001，38（8）：923- 926.
［2］陈建平. 矩阵三角分解的递归算法［J］.南通工学院学报（自然科学版），20 03，2(4):1-3.
?CHEN Jianping. Recursive algorithm for matrix triangular factorization ［J］. Jo urnal of Nantong Institute of Technology (natural science),2003, 2(4):1-3.
［3］LIU Mode. The structured programming of Crouts method solving line ar equation ［J］.Journal of Sanming College,2003,20(2):62-66.
［4］智慧来,张礼达. 矩阵的Crout递归分解算法及程序设计［J］.西华大学学报( 自然科学版),2006，25(3)：48-50.
ZHI Huilai, ZHANG Lida. Recursive algorithm and programming for matrix Crout′s factorization ［J］.Journal of Xihua University (natural science),2006,25
【5】徐仲，张凯院，陆全,等. 矩阵论简明教程［M］.北京：科学出版社，2002.
［6］RICHARD L, BURDEN J, FAIRES D. Numerical analysis :7th Edition ［M］.Thomson Learning,2001.
［7］JAIN S K ,GUNAWARDENA A D. Linear algebra: an interactive approach ［M］. Beijing: China Machine Press,2003.
［8］智东杰. 按定义计算行列式及余子式的C语言递归程序设计［J］. 中国教育教学研究杂志,2004,3(12): 79-80.
?ZHI Dongjie. C language recursive programming of computing determinant and compl ement minor according to their definitions ［J］.The Research Magazine of Educat ion and Teach in China,2004,3(12):79-80.
［9］郑桂水. Mathcad 2000 实用教程［M］.北京：国防工业出版社，2000.
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备注/Memo
收稿日期：2006-04-27.
作者简介：智东杰，男，1952年生，中国科技研究交流中心研究员，主要研究方向为人工智能、符号计算.E-mai: zhidongjie@126.com；智慧来，男，1981年生，硕士研究生，主要研究方向为计算智能在水电站经济运行中的应用.
更新日期/Last Update:
2009-05-05