极分解的一类近似计算与比较

基于级数展开给出了极分解中右伸长张量U的级数表示,通过对级数项的选取得到右伸长张量的不同近似表达式.针对不同级数展开表示,得到表达式最小误差的级数展开形式.进而结合一些简单实例,验证了近似公式的有效性.最后与文献[1]关于计算右伸长张量U和转动张量R的近似表达式进行了比较,本文的级数展开方式得到的右伸长张量U和转动张量R的近似表达式不但简洁,而且计算精度更高、适用范围更广.

A CLASS OF APPROXIMATE CALCULATION OF POLAR DECOMPOSITION AND THE CORRESPONDING COMPARISON

Based on the series expansion,the series forms of right stretch tensor in polar decomposition are given,and the different approximate expressions of right stretch tensor are obtained by selecting different number of series terms.From the different expressions,the series expansion with the least error is found.The effectiveness of the approximate expression is verified using some simple examples.Compared with the approximate expressions of right stretch tensor U and rotation tensor R proposed by Ref.[1],the approximate expressions of right stretch tensor U and rotation tensor R given in this paper are of simple forms,high accurate and widely applicability.