کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8897765 | 1631042 | 2018 | 21 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On two generalized inverse eigenvalue problems for Hessenberg-upper triangular pencils and their application to the study of GMRES convergence
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله

چکیده انگلیسی
We discuss two generalized inverse eigenvalue problems. The first one: For a given unreduced upper Hessenberg matrix H, find a nonsingular upper triangular matrix T such that all the pencils HkâλTk have prescribed eigenvalues, where Hk and Tk are the leading kÃk principal submatrices of H and T, respectively. The second one: For a given unitary unreduced upper Hessenberg matrix Q, find a nonsingular upper triangular matrix T such that all the pencils TkâθQkâ have prescribed eigenvalues, where Tk is the leading kÃk principal submatrix of T, and Qkâ is the conjugate transpose of the leading kÃk principal submatrix of Q. We present the necessary and sufficient conditions for the solvability of the two problems. Our results lead to an alternative proof for the statement that any admissible Ritz value set or admissible harmonic Ritz value set is possible for the prescribed GMRES residual norms. Here, the term “admissible” means there are some restrictions on the sets if GMRES stagnates at some iterations.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 553, 15 September 2018, Pages 16-36
Journal: Linear Algebra and its Applications - Volume 553, 15 September 2018, Pages 16-36
نویسندگان
Kui Du, Yunqing Huang, Yiwei Wang,