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An Iterative Algorithm for Solving the Least-Squares Problem of Matrix Equation AXB+CYD=E
Kai-juan Shen,Chuan-hua You,Yu-xia Du 한국전산응용수학회 2008 Journal of applied mathematics & informatics Vol.26 No.5
In this paper, an iterative method is proposed to solve the least-squares problem of matrix equation AXB + CY D = E over un-known matrix pair [X, Y ]. By this iterative method, for any initial matrix pair [X1, Y1], a solution pair or the least-norm least-squares solution pair of which can be obtained within finite iterative steps in the absence of roundoff errors. In addition, we also consider the optimal approximation problem for the given matrix pair [X0, Y0] in Frobenius norm. Given numerical examples show that the algorithm is efficient. In this paper, an iterative method is proposed to solve the least-squares problem of matrix equation AXB + CY D = E over un-known matrix pair [X, Y ]. By this iterative method, for any initial matrix pair [X1, Y1], a solution pair or the least-norm least-squares solution pair of which can be obtained within finite iterative steps in the absence of roundoff errors. In addition, we also consider the optimal approximation problem for the given matrix pair [X0, Y0] in Frobenius norm. Given numerical examples show that the algorithm is efficient.
AN ITERATIVE ALGORITHM FOR SOLVING THE LEAST-SQUARES PROBLEM OF MATRIX EQUATION AXB+CYD=E
Shen, Kai-Juan,You, Chuan-Hua,Du, Yu-Xia Korean Society of Computational and Applied Mathem 2008 Journal of applied mathematics & informatics Vol.26 No.5
In this paper, an iterative method is proposed to solve the least-squares problem of matrix equation AXB+CYD=E over unknown matrix pair [X, Y]. By this iterative method, for any initial matrix pair [$X_1,\;Y_1$], a solution pair or the least-norm least-squares solution pair of which can be obtained within finite iterative steps in the absence of roundoff errors. In addition, we also consider the optimal approximation problem for the given matrix pair [$X_0,\;Y_0$] in Frobenius norm. Given numerical examples show that the algorithm is efficient.
Profiling Gene Expression During Gland Morphogenesis of a Glanded and a Glandless Upland Cotton
Ying-Fan Cai,Min Chen,Quan Sun,Yong-Fang Xie,Sheng-Wei Li,Jian-Chuan Mo,Ming-Feng Jiang,You-Lu Yuan,Yu-Zhen Shi,Huai-Zhong Jiang,Zheng Pan,Yun-Ling Gao,Peng-Sheng Ye,Hua-Lan Zeng 한국식물학회 2009 Journal of Plant Biology Vol.52 No.6
The pigment gland is an important character of the Gossypium plant. With the aim of identifying genes involved in pigment gland morphogenesis in cotton, gene expression during pigment gland morphogenesis in Chuan 2802, which is glanded both in seed and plant, and a glandless line N5 was profiled using Affymetrix Cotton microarray. The results showed that there were 564 differentially expressed genes greater than twofold during gland morphogenesis. About 60.2% of these genes shares similarity with known genes on GenBank and about 39.8% with no functional description in the database. These described genes may play roles in defense response, response to oxidative stress, peroxidase activity, and the other metabolic pathways. The KEGG Orthology-Based Annotation System indicated that these above twofold expressed genes involved seven biochemical pathways on KEGG. These findings suggest that a complicated regulation is associated with pigment gland morphogenesis and the associated defense response including gossypol biosynthesis in cotton.