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Jan
1
comment Is there a faster algorithm than $O(n^2)$ for calculating “cofactors” $C_k = \prod\limits_{j\neq k}(c_k - c_j)$?
could you elaborate?
Jan
1
comment Is there a faster algorithm than $O(n^2)$ for calculating “cofactors” $C_k = \prod\limits_{j\neq k}(c_k - c_j)$?
yeah, vectorization is another option. (I'm using numpy in my case.) But the polynomial coefficients are huge and are ill-conditioned; I have to work with the roots directly in order to keep numerical errors low.
Jan
1
revised Is there a faster algorithm than $O(n^2)$ for calculating “cofactors” $C_k = \prod\limits_{j\neq k}(c_k - c_j)$?
added 289 characters in body
Jan
1
asked Is there a faster algorithm than $O(n^2)$ for calculating “cofactors” $C_k = \prod\limits_{j\neq k}(c_k - c_j)$?
Dec
23
accepted residue equation for the denominator in a Padé approximant for $e^{-x}$
Dec
23
accepted solving a series of nonlinear equations for the zeros of Bessel polynomials
Dec
20
revised residue equation for the denominator in a Padé approximant for $e^{-x}$
added 22 characters in body
Dec
20
revised residue equation for the denominator in a Padé approximant for $e^{-x}$
added 889 characters in body
Dec
20
answered residue equation for the denominator in a Padé approximant for $e^{-x}$
Dec
20
revised residue equation for the denominator in a Padé approximant for $e^{-x}$
added 69 characters in body
Dec
20
asked residue equation for the denominator in a Padé approximant for $e^{-x}$
Dec
20
answered solving a series of nonlinear equations for the zeros of Bessel polynomials
Dec
19
comment solving a series of nonlinear equations for the zeros of Bessel polynomials
more info on Bessel polynomials at dlmf.nist.gov/18.34
Dec
19
asked solving a series of nonlinear equations for the zeros of Bessel polynomials
Dec
18
comment roots of Padé approximating polynomials to the exponential function
and Gonnet/Guettel/Trefethen's paper which also seems very relevant but I can't figure out how to apply it: guettel.com/download/gonnet_guettel_trefethen.pdf which I
Dec
18
accepted Finding a similarity transform for a matrix that minimizes the (2-norm) condition number
Dec
18
comment roots of Padé approximating polynomials to the exponential function
Then we have Saff and Varga's paper On the Zeros and Poles of Padé Approximants to $e^z$ which looks tantalizingly relevant, but they don't compute the roots numerically, they just have proofs of general behavioral of where they are and aren't.
Dec
18
revised roots of Padé approximating polynomials to the exponential function
added 668 characters in body; edited tags
Dec
17
asked roots of Padé approximating polynomials to the exponential function
Dec
17
accepted Eigenvectors of special matrix with characteristic polynomial