Yazar "Turkmen, Ramazan" seçeneğine göre listele

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    Improved upper bounds for the solution of the continuous algebraic Riccati matrix equation
    (ELSEVIER SCIENCE INC, 2013) Ulukok, Zubeyde; Turkmen, Ramazan
    In this paper, we present upper bounds for the solution matrix of the continuous algebraic Riccati matrix equation (CARE) by utilizing some matrix inequalities and linear algebraic techniques. Also, for the derived each bounds, iterative algorithms are developed to obtain tighter solution estimates. Having compared some appearing results in the literature, the obtained bounds are less restrictive and more efficient. Finally, numerical examples are given to illustrate the effectiveness of the proposed results. (C) 2013 Elsevier Inc. All rights reserved.
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    INEQUALITIES OF GENERALIZED MATRIX FUNCTIONS VIA TENSOR PRODUCTS
    (INT LINEAR ALGEBRA SOC, 2014) Paksoy, Vehbi E.; Turkmen, Ramazan; Zhang, Fuzhen
    By an embedding approach and through tensor products, some inequalities for generalized matrix functions (of positive semidefinite matrices) associated with any subgroup of the permutation group and any irreducible character of the subgroup are obtainned.
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    New upper bounds on the solution matrix to the continuous algebraic Riccati matrix equation
    (PERGAMON-ELSEVIER SCIENCE LTD, 2013) Ulukok, Zubeyde; Turkmen, Ramazan
    In this paper, new upper bounds for the solution matrix of the continuous algebraic Riccati matrix equation (CARE) are derived by means of some matrix inequalities and linear algebraic techniques. Furthermore, for the derived each bound, iterative algorithms are developed to obtain sharper solution estimates. Comparing with some appearing results in the literature, the presented bounds are less restrictive and more efficient. Finally, numerical examples are given to illustrate the effectiveness of the proposed results. (C) 2013 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
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    Notes on the (s, t)-Lucas and Lucas Matrix Sequences
    (CHARLES BABBAGE RES CTR, 2008) Civciv, Haci; Turkmen, Ramazan
    In this article, defining the matrix extensions of the Fibonacci and Lucas numbers we start a new approach to derive formulas for some integer numbers which have appeared, often surprisingly, as answers to intricate problems, in conventional and in recreational Mathematics. Our approach provides a new way of looking at integer sequences from the perspective of matrix algebra, showing how several of these integer sequences relate to each other.
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    On the (s,t)-fibonacci and fibonacci matrix sequences
    (CHARLES BABBAGE RES CTR, 2008) Civciv, Haci; Turkmen, Ramazan
    It is always fascinating to see what results when seemingly different areas mathematics overlap. This article reveals one such result; number theory and linear algebra are intertwined to yield complex factorizations of the classic Fibonacci, Pell, Jacobsthal, and Mersenne numbers. Also, in this paper we define a new matrix generalization of the Fibonacci numbers, and using essentially a matrix approach we show some properties of this matrix sequence.
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    On the spectral norm of r-circulant matrices with the Pell and Pell-Lucas numbers
    (SPRINGER INTERNATIONAL PUBLISHING AG, 2016) Turkmen, Ramazan; Gokbas, Hasan
    Let us define A = C-r (a(0), a(1),..., a(n-1)) to be a nxn r-circulant matrix. The entries in the first row of A = C-r (a(0), a(1),..., a(n-1)) are a(i) = P-i, a(i) = Q(i), a(i) = P-i(2) or a(i) = Q(i)(2) (i = 0, 1, 2,..., n - 1), where P-i and Q(i) are the ith Pell and Pell-Lucas numbers, respectively. We find some bounds estimation of the spectral norm for r-Circulant matrices with Pell and Pell-Lucas numbers.
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    Refinements of Hermite-Hadamard type inequalities for operator convex functions
    (SPRINGER INTERNATIONAL PUBLISHING AG, 2013) Bacak, Vildan; Turkmen, Ramazan
    The purpose of this paper is to present some new versions of Hermite-Hadamard type inequalities for operator convex functions. We give refinements of Hermite-Hadamard type inequalities for convex functions of self-adjoint operators in a Hilbert space analogous to well-known inequalities of the same type. The results presented in this paper are more general than known results given by several authors.
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    Some norm inequalities for special Gram matrices
    (DE GRUYTER OPEN LTD, 2016) Turkmen, Ramazan; Kan, Osman; Gokbas, Hasan
    In this paper we firstly give majorization relations between the vectors F-n = {f(0), f(1),..., f(n-1)}, L-n = {l(0), l(1),..., l(n-1)} and P-n = {p(0), p(1),..., p(n-1) g which constructed with fibonacci, lucas and pell numbers. Then we give upper and lower bounds for determinants, Euclidean norms and Spectral norms of Gram matrices G(F) = < F-n, F-n >, G(L) = < L-n, L-n >, G(P) = < P-n, P-n >, G(FL) = < F-n, L-n >, G(FP) = < F-n, P-n >.
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    Some Upper Matrix Bounds for the Solution of the Continuous Algebraic Riccati Matrix Equation
    (HINDAWI PUBLISHING CORPORATION, 2013) Ulukok, Zubeyde; Turkmen, Ramazan
    We propose diverse upper bounds for the solution matrix of the continuous algebraic Riccati matrix equation (CARE) by building the equivalent form of the CARE and using some matrix inequalities and linear algebraic techniques. Finally, numerical example is given to demonstrate the effectiveness of the obtained results in this work as compared with some existing results in the literature. These new bounds are less restrictive and provide more efficient results in some cases.