کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4603554 1336964 2008 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Least squares solutions to AX = B for bisymmetric matrices under a central principal submatrix constraint and the optimal approximation
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Least squares solutions to AX = B for bisymmetric matrices under a central principal submatrix constraint and the optimal approximation
چکیده انگلیسی

A matrix A∈Rn×n is called a bisymmetric matrix if its elements ai,j satisfy the properties ai,j=aj,i and ai,j=an-j+1,n-i+1 for 1⩽i,j⩽n. This paper considers least squares solutions to the matrix equation AX=B for A under a central principal submatrix constraint and the optimal approximation. A central principal submatrix is a submatrix obtained by deleting the same number of rows and columns in edges of a given matrix. We first discuss the specified structure of bisymmetric matrices and their central principal submatrices. Then we give some necessary and sufficient conditions for the solvability of the least squares problem, and derive the general representation of the solutions. Moreover, we also obtain the expression of the solution to the corresponding optimal approximation problem.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 428, Issue 4, 1 February 2008, Pages 871-880