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On the Reduction of a Complex Matrix to Triangular or Diagonal by Consimilarity
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作者 Tongsong Jiang musheng wei 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 2006年第2期107-112,共6页
Two n × n complex matrices A and B are said to be consimilar if S?1AS = B for some nonsingular n × n complex matrix S. This paper, by means of real representation of a complex matrix, studies problems of red... Two n × n complex matrices A and B are said to be consimilar if S?1AS = B for some nonsingular n × n complex matrix S. This paper, by means of real representation of a complex matrix, studies problems of reducing a given n × n complex matrix A to triangular or diagonal form by consimilarity, not only gives necessary and su?cient conditions for contriangularization and condiagonalization of a complex matrix, but also derives an algebraic technique of reducing a matrix to triangular or diagonal form by consimilarity. 展开更多
关键词 实表示 复矩阵 三角形 对角线
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A NUMERICALLY STABLE BLOCK MODIFIED GRAM-SCHMIDT ALGORITHM FOR SOLVING STIFF WEIGHTED LEAST SQUARES PROBLEMS 被引量:2
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作者 musheng wei Qiaohua Liu 《Journal of Computational Mathematics》 SCIE EI CSCD 2007年第5期595-619,共25页
Recently, Wei in proved that perturbed stiff weighted pseudoinverses and stiff weighted least squares problems are stable, if and only if the original and perturbed coefficient matrices A and A^- satisfy several row r... Recently, Wei in proved that perturbed stiff weighted pseudoinverses and stiff weighted least squares problems are stable, if and only if the original and perturbed coefficient matrices A and A^- satisfy several row rank preservation conditions. According to these conditions, in this paper we show that in general, ordinary modified Gram-Schmidt with column pivoting is not numerically stable for solving the stiff weighted least squares problem. We then propose a row block modified Gram-Schmidt algorithm with column pivoting, and show that with appropriately chosen tolerance, this algorithm can correctly determine the numerical ranks of these row partitioned sub-matrices, and the computed QR factor R^- contains small roundoff error which is row stable. Several numerical experiments are also provided to compare the results of the ordinary Modified Gram-Schmidt algorithm with column pivoting and the row block Modified Gram-Schmidt algorithm with column pivoting. 展开更多
关键词 Weighted least squares STIFF Row block MGS QR Numerical stability Rank preserve.
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