کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5775657 | 1631741 | 2017 | 14 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Rank/inertia approaches to weighted least-squares solutions of linear matrix equations
ترجمه فارسی عنوان
رویکرد رتبه / درونی به مقادیر کمترین مربعات وزن معادلات ماتریس خطی
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
چکیده انگلیسی
The well-known linear matrix equation AX=B is the simplest representative of all linear matrix equations. In this paper, we study quadratic properties of weighted least-squares solutions of this matrix equation. We first establish two groups of closed-form formulas for calculating the global maximum and minimum ranks and inertias of matrices in the two quadratical matrix-valued functions Q1âXP1Xâ² and Q2âXâ²P2X subject to the restriction trace[(AXâB)â²W(AXâB)]=min, where both Pi and Qi are real symmetric matrices, i=1,2, W is a positive semi-definite matrix, and Xâ² is the transpose of X. We then use the rank and inertia formulas to characterize quadratic properties of weighted least-squares solutions of AX=B, including necessary and sufficient conditions for weighted least-squares solutions of AX=B to satisfy the quadratic symmetric matrix equalities XP1Xâ²=Q1 an Xâ²P2X=Q2, respectively, and necessary and sufficient conditions for the quadratic matrix inequalities XP1Xâ²â»Q1â(â½Q1,ââºQ1,ââ¼Q1) and Xâ²P2Xâ»Q2â(â½Q2,ââºQ2,ââ¼Q2) in the Löwner partial ordering to hold, respectively. In addition, we give closed-form solutions to four Löwner partial ordering optimization problems on Q1âXP1Xâ² and Q2âXâ²P2X subject to weighted least-squares solutions of AX=B.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 315, 15 December 2017, Pages 400-413
Journal: Applied Mathematics and Computation - Volume 315, 15 December 2017, Pages 400-413
نویسندگان
Bo Jiang, Yongge Tian,