Semidefinite Approximations of the Matrix Logarithm
نویسندگان
چکیده
منابع مشابه
Semidefinite approximations of the matrix logarithm
We propose a new way to treat the exponential/relative entropy cone using symmetric cone solvers. Our approach is based on highly accurate rational (Padé) approximations of the logarithm function. The key to this approach is that our rational approximations, by construction, inherit the (operator) concavity of the logarithm. Importantly, our method extends to the matrix logarithm and other deri...
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15 صفحه اولEvaluating Padé Approximants of the Matrix Logarithm
The inverse scaling and squaring method for evaluating the logarithm of a matrix takes repeated square roots to bring the matrix close to the identity, computes a Padé approximant, and then scales back. We analyze several methods for evaluating the Padé approximant, including Horner’s method (used in some existing codes), suitably customized versions of the Paterson– Stockmeyer method and Van L...
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ژورنال
عنوان ژورنال: Foundations of Computational Mathematics
سال: 2018
ISSN: 1615-3375,1615-3383
DOI: 10.1007/s10208-018-9385-0