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- W2038696008 abstract "We present a semidefinite programming approach for computing optimally conditioned positive definite Hankel matrices of order n . Unlike previous approaches, our method is guaranteed to find an optimally conditioned positive definite Hankel matrix within any desired tolerance. Since the condition number of such matrices grows exponentially with n , this is a very good test problem for checking the numerical accuracy of semidefinite programming solvers. Our tests show that semidefinite programming solvers using fixed double precision arithmetic are not able to solve problems with n > 30 . Moreover, the accuracy of the results for 24 ⩽ n ⩽ 30 is questionable. In order to accurately compute minimal condition number positive definite Hankel matrices of higher order, we use a Mathematica 6.0 implementation of the SDPHA solver that performs the numerical calculations in arbitrary precision arithmetic. By using this code, we have validated the results obtained by standard codes for n ⩽ 24 , and we have found optimally conditioned positive definite Hankel matrices up to n = 100 ." @default.
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- W2038696008 date "2010-11-01" @default.
- W2038696008 modified "2023-09-28" @default.
- W2038696008 title "Minimal condition number for positive definite Hankel matrices using semidefinite programming" @default.
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- W2038696008 doi "https://doi.org/10.1016/j.laa.2010.04.052" @default.
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