کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4599870 | 1336826 | 2013 | 19 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On condition numbers of a basis
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
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چکیده انگلیسی
The condition number κp(x̲) of an ordered basis x̲ of a finite dimensional subspace of an Lp-space, 1⩽p⩽â, measures the extent to which small relative changes in the basis coefficients lead to small relative changes in the function values, and vice versa. We consider an ordered basis x̲ of an arbitrary finite dimensional normed space and introduce numbers Ï°p,r(x̲), 1⩽p,r⩽â, which control 'near linear dependence' of the basis elements as well as overflow/underflow during computations. These numbers are defined in terms of the norms of the basis elements and the norms of the elements of the ordered dual basis. Optimal scaling strategies are determined. Effects of matrix transformation on these numbers are explored. If x̲ is an ordered basis of an inner product space, then Ï°p,r(x̲) can be calculated explicitly in terms of the diagonal entries of the Gram matrix corresponding to x̲ and the diagonal entries of its inverse. In the last section, we define a condition number of x̲ relative to the problem of computing the ordered dual basis, and relate it to Ï°p,q(x̲), where (1/p)+(1/q)=1.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 439, Issue 11, 1 December 2013, Pages 3359-3377
Journal: Linear Algebra and its Applications - Volume 439, Issue 11, 1 December 2013, Pages 3359-3377
نویسندگان
Mario Ahues, Balmohan V. Limaye,