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《Chinese Journal of Geophysics》 1992-02
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ITERATIVE ALGORITHM OF REDUCING DEMINSIONS

XIONG FU-LIN (Nonferrous Metal Geological Research Institute of Guangxi, Nanning 530031)GUAN ZHI-NING(China University of Geosciences, Beijing 100083)  
The paper presents the method of solving huge linearly equations AX = b (where A∈Rn×n is symmetrical positive metrix) by iterative algorithm of reducing demin-sions. Means of reducing deminsions is that value range of unknown vector X in the huge linearly equations is limited to the subspace whith is defined by k linearly independent vectors which are selected from n deminsion space and that the linearly equations with n unknown numbers is reduced the linearly equations with k unknown unmbers. Solving the linearly equations with k unknown numbers, the optimal solution of X is obtained in the subspace. From the optimal solution, the other k linearly independent vectors are selected from n deminsion space and the linearly equations with n unknown numbers is reduced to linearly equations with k unknown numbers So the iterative algorithm of reducing deminsions is formed.
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【References】
Chinese Journal Full-text Database 1 Hits
1 LI JIA-KANG;JIANG LAN-YIN;LIU YU(Research,Institute of petroleum Exploration and Development, Geophysics Department, Beijing 100083);A COMPARISON OF DESCENDING DIMENSION ALGORITHM WITH CONJUGATE GRADIENT METHOD AND SVD[J];Chinese Journal of Geophysics;1994-S2
【Co-references】
Chinese Journal Full-text Database 3 Hits
1 YANG WEN-CAI(Beijing Computer Center, Ministry of Geology and Mineral Resources);A GENERALIZED INVERSION TECHNIQUE FOR POTENTIAL FIELD DATA PROCESSING[J];Chinese Journal of Geophysics;1986-03
2 HUANG HAO-PING(Changchun University of Earth Sciences, Changchun 130026);ELECTROMAGNETIC DATA PROCESSING USING THE SINGULAR VALUE DECOMPOSITION[J];Chinese Journal of Geophysics;1991-05
3 Du JIAN-YUAN YANG WEN-CAI(Beijing Computer Center of Geology, Beijing 100083);CASCADE APPROACH FOR CROSS-HOLE SEISMIC TOMOGRAPHY[J];Chinese Journal of Geophysics;1991-06
【Secondary References】
Chinese Journal Full-text Database 3 Hits
1 JIN Long1, CHEN Xiao-hong1, LIU Qi-cheng 1, 2 (1. School of Resources and Information , University of Petroleum, Beijing 102249, China; 2. School of Computer technology , University of Yantai, Yantai 264005, China);New method for time-lapse seismic matching based on SVD[J];Progress In Geophysics;2005-02
2 LIU Hai-fei1,RUAN Bai-yao2,LIU Jian-xin1(1.School of Info-Physics and Geomatics Engineering,Central South University,Changsha 410083,China;2.Department of Resources and Environment Engineering,Guilin Institute of Technology,Gulin 541004,China);The conjugate gradient algorithm of variational damping and its capability analysis[J];Progress in Geophysics;2008-01
3 LI PING HSU HOU-TZE Institute of Geodesy and Geophysics,CAS, Wuhan 430077, China Seismological Bureau of Liaoning Provinec,Shenyang 110031, China;ROBUST ESTIMATION PLUS PSEUDO-INVERSE METHOD IN GEOPHYSICAL INVERSION[J];Chinese Journal of Geophysics;2000-02
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