12 авг. 2020 г. · Wilkinson's polynomial is ill conditioned because of the huge ratio of the error in the solution to an error in the data. The ratio you cite is ...

17 янв. 2024 г. · The derivative of p(x)=∏nk=1(x−αk) is p′(αm)=limx→αmp(x)−0x−αm=∏k≠m(αm−αk).

9 янв. 2016 г. · Suppose that we perturb a polynomial p(x)=Π(x−αj) with roots αj by adding a small multiple t·c(x) of a polynomial c(x), and ask how this affects ...

12 сент. 2011 г. · Adding or subtracting that to the coefficient of x19 in Wilkinson's polynomial gets you complex roots. – J. M. ain't a mathematician.

19 апр. 2015 г. · How do existing roots of a polynomial change when adding higher-order term with a small coefficient? Given a sufficiently small coefficient of ...

14 апр. 2018 г. · You should read about Wilkinson's polynomial, though it is of degree 20.. All its roots are real and well separated, but perturbing one ...

7 нояб. 2014 г. · This question seems related to the Wilkinson Polynomial where Wilkinson shows that small changes to polynomial coefficients can have large effects on its zeros.

9 сент. 2011 г. · Wilkinson's polynomial suggests that continuity may not prevent instability/ill-conditioning. – Henry. Commented Sep 10, 2011 at 17:23. 6. A ...

8 мар. 2023 г. · In Wikipedia, there is a list of popular test functions for optimization problems https://en.wikipedia.org/wiki/Test_functions_for_optimization, ...

16 июл. 2017 г. · You can have real roots becoming complex or the other way around by slightly changing a polynomial's coefficients. James Wilkinson is one of the ...