On symmetric decompositions of positive operators
نویسندگان
چکیده
منابع مشابه
Positive Decompositions of Exponential Operators
The solution of many physical evolution equations can be expressed as an exponential of two or more operators. Approximate solutions can be systematically derived by decomposing the exponential in a product form. For time-reversible equations, such as the Hamilton or the Schrödinger equation, it is immaterial whether the decomposition coefficients are positive or negative. For timeirreversible ...
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Let H be a complex Hilbert space. Denote by B(H)+ the set of all positive bounded linear operators on H. A bijective map φ : B(H)+ → B(H)+ is said to preserve Lebesgue decompositions in both directions if for any quadruple A,B,C,D of positive operators, B = C +D is an A-Lebesgue decomposition of B if and only if φ(B) = φ(C)+φ(D) is a φ(A)-Lebesgue decomposition of φ(B). It is proved that every ...
متن کاملStructure of positive decompositions of exponential operators.
The solution of many physical evolution equations can be expressed as an exponential of two or more operators acting on initial data. Accurate solutions can be systematically derived by decomposing the exponential in a product form. For time-reversible equations, such as the Hamilton or the Schrödinger equation, it is immaterial whether or not the decomposition coefficients are positive. In fac...
متن کاملComment on "Structure of positive decompositions of exponential operators".
An elementary proof is shown on the necessary existence of negative coefficients in splitting methods of order p > or = 3.
متن کاملThe Structure of Positive Decompositions of Exponential Operators
The solution of many physical evolution equations can be expressed as an exponential of two or more operators acting on initial data. Accurate solutions can be systematically derived by decomposing the exponential in a product form. For time-reversible equations, such as the Hamilton or the Schrödinger equation, it is immaterial whether or not the decomposition coefficients are positive. In fac...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2017
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8121/aa6469