کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8897731 1631040 2018 6 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Another orthogonal matrix, revisited
ترجمه فارسی عنوان
یکی دیگر از ماتریس متعامد، بازبینی شده است
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی
A 2006 paper by Parlett and Barszcz [4] proposed the following problem: Given an unit vector q, compute the orthogonal Hessenberg matrix A with first column q. In complex form, this translates to completing the unitary Hessenberg matrix U with first column q. Looking at the matrix Iâqqâ in the special form Iâqqâ=LD2Lâ, where L is nÃ(nâ1) and lower triangular with 1's on its main diagonal and D2=diag(Î¼12,â¦,Î¼nâ12) is positive definite, Parlett observed that for i>j the entries of LË=LD can be written as lËij=âqiqâ¾jÎ¼j/Ïj, where qâ¾j denotes the complex conjugate of qj and Ïi=âj=i+1n|qj|2, Ïn=0, and Î¼i=Ïi/Ïiâ1, for i=1,â¦,n. Furthermore, one solution to this problem is U=[qLË]. Section 1 provides some background, as well as details on the derivation of Parlett's formula. Section 2 contains the main result, where Parlett's method is extended to “tall thin” matrices as suggested by Parlett in his original paper. In other words, using a repeated application of Parlett's method, a solution is given to the problem of completing the unitary k-Hessenberg matrix given its first k columns.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 555, 15 October 2018, Pages 355-360
نویسندگان
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