摘要
研究矩阵原位替换解算方法,包括矩阵行列式、矩阵方程未知数和矩阵逆阵的解算。利用矩阵三角分解原理和矩阵运算的基本法则导出矩阵元素约化值的计算公式,从而进一步导出利用矩阵元素约化值计算矩阵行列式、矩阵方程未知数和矩阵逆阵元素的原位替换解算公式。解算公式用纯量形式表出,有利于编程计算,且可实现按矩阵元素在矩阵中的存储位置原位替换解算。该解算方法可节省计算用内存空间和时间,提高科学计算的效率。
The calculation methods of matrix in-situ replacement are researched, including the matrix determinant, the matrix equation unknown and the matrix inversion computation. Making use of the principle of matrix triangular decomposition and matrix operations fundamental to derive the calculation formula for matrix elements of simplification value, it further derives using of matrix ele- ments of simplification value to compute the in-situ replacement solution formula of calculation of matrix determinant, matrix equation unknown and inverse matrix array elements. Calculation of the formula used in pure form of presentation is conducive to programming calculation, and it can realize the in-situ replacement solution according to the place of matrix elements in the matrix. The calculation space and time of this method can be saved, the efficiency of scientific computation is improved.
出处
《测绘科学》
CSCD
北大核心
2009年第4期30-33,共4页
Science of Surveying and Mapping
基金
黑龙江省自然科学基金项目(A200505)
黑龙江空间地理信息省级重点实验室项目(zk200606)
关键词
矩阵
原位替换
快速解算
matrix
in-situ replacement
fast calculation
