کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9501283 | 1338396 | 2005 | 42 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The shifted number system for fast linear algebra on integer matrices
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: The shifted number system for fast linear algebra on integer matrices The shifted number system for fast linear algebra on integer matrices](/preview/png/9501283.png)
چکیده انگلیسی
The shifted number system is presented: a method for detecting and avoiding error producing carries during approximate computations with truncated expansions of rational numbers. Using the shifted number system the high-order lifting and integrality certification techniques of Storjohann 2003 for polynomial matrices are extended to the integer case. Las Vegas reductions to integer matrix multiplication are given for some problems involving integer matrices: the determinant and a solution of a linear system can be computed with about the same number of bit operations as required to multiply together two matrices having the same dimension and size of entries as the input matrix. The algorithms are space efficient.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Complexity - Volume 21, Issue 4, August 2005, Pages 609-650
Journal: Journal of Complexity - Volume 21, Issue 4, August 2005, Pages 609-650
نویسندگان
Arne Storjohann,