کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4637383 | 1340739 | 2006 | 17 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Computing real roots of a polynomial in Chebyshev series form through subdivision with linear testing and cubic solves
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Computing real roots of a polynomial in Chebyshev series form through subdivision with linear testing and cubic solves Computing real roots of a polynomial in Chebyshev series form through subdivision with linear testing and cubic solves](/preview/png/4637383.png)
چکیده انگلیسی
An arbitrary polynomial of degree N, fN(x), can always be represented as a truncated Chebyshev polynomial series (“Chebyshev form”). This representation is much better conditioned than the usual “power form” of a polynomial. We describe a new method for finding the real roots of fN(x) in Chebyshev form. The canonical interval, x ∈ [−1, 1], is subdivided into Ns subintervals. Each is tested for zeros using the error bound for linear interpolation. On “zero-possible” intervals, fN is approximated by a cubic polynomial, whose roots are then found by the usual sixteenth century formulas.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 174, Issue 2, 15 March 2006, Pages 1642–1658
Journal: Applied Mathematics and Computation - Volume 174, Issue 2, 15 March 2006, Pages 1642–1658
نویسندگان
John P. Boyd,