Retraction Note to: Factorization of Triangular Matrix-Functions of an Arbitrary Order
نویسندگان
چکیده
منابع مشابه
Almost periodic factorization of certain block triangular matrix functions
Let G(x) = [ eIm 0 c−1e−iνx + c0 + c1e e−iλxIm ] , where cj ∈ Cm×m, α, ν > 0 and α+ ν = λ. For rational α/ν such matrices G are periodic, and their Wiener-Hopf factorization with respect to the real line R always exists and can be constructed explicitly. For irrational α/ν, a certain modification (called an almost periodic factorization) can be considered instead. The case of invertible c0 and ...
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Factorizations of Wiener–Hopf type are considered in the abstract framework of Wiener algebras of matrix-valued functions on connected compact abelian groups, with a non-archimedean linear order on the dual group. A criterion for factorizability is established for 2 × 2 block triangular matrix functions with elementary functions on the main diagonal and a binomial expression in the off-diagonal...
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In various applications, it is necessary to differentiate a matrix functional w(A(x)), where A(x) is a matrix depending on a parameter vector x. Usually, the functional itself can be readily computed from a triangular factorization of A(x). This paper develops several methods that also use the triangular factorization to efficiently evaluate the first and second derivatives of the functional. B...
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A large portion of Linear algebra (scientific computing) is devoted to accelerate computationally intensive operations through the deeper understanding on the structure of the matrix. While it is not extremely hard to obtain an analytical solutions for the problems of interest, often a large-size matrix or repetetive nature of the computations prohibit us from getting the actual solution in num...
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ژورنال
عنوان ژورنال: Lobachevskii Journal of Mathematics
سال: 2019
ISSN: 1995-0802,1818-9962
DOI: 10.1134/s1995080219010153