Matrix Theory and Algorithms

In this paper, we introduce and investigate a new class of r-circulant matrices whose entries are generated by higher-order Fibonacci numbers. Explicit representations of the eigenvalues of these matrices are derived by means of the Binet formula together with the structural properties of r-circulant matrices. Based o…

Bu çalışmada, birinci mertebeden lineer gecikmeli diferansiyel denklemler için başlangıç değer probleminin çözümü için yeni bir nümerik şema önerilmiştir. Bu şema, kalan terimleri integral formda olan quadratür kuralları kullanarak düzgün bir şebeke üzerinde sonlu farklar yöntemi ile oluşturulmuştur. Şemanın ayrık mak…

Bu çalışmada, birinci mertebeden lineer gecikmeli diferansiyel denklemler için başlangıç değer probleminin çözümü için yeni bir nümerik şema önerilmiştir. Bu şema, kalan terimleri integral formda olan quadratür kuralları kullanarak düzgün bir şebeke üzerinde sonlu farklar yöntemi ile oluşturulmuştur. Şemanın ayrık mak…

In [T. Boros, P. Rozsa, Linear Algebra Appl., 421 (2007), 407–416.], the authors showed that for the Sylvester–Kac matrix of odd order, $ 2n+1 $ ($ n\ge0 $), $ n $ of the squared singular values were integers. We present a variation of this matrix for which analogous results are obtained in both the odd- and even-orde…

Rasmussen's permanent estimator is a simple and unbiased estimator for the permanent of a binary matrix, but its practical performance can be limited by trajectories that terminate before completing a perfect matching. These failed trajectories, together with dispersion among the surviving weights, can substantially r…

We study copositive matrices which admit a decomposition into a sum of a positive semidefinite matrix and a matrix with nonnegative entries. Our main result shows that if the off-diagonal entries of a copositive matrix are nondecreasing in rows and in columns, then it admits such a decomposition. We apply this result…

We study copositive matrices which admit a decomposition into a sum of a positive semidefinite matrix and a matrix with nonnegative entries. Our main result shows that if the off-diagonal entries of a copositive matrix are nondecreasing in rows and in columns, then it admits such a decomposition. We apply this result…

Matrix valued (asymmetric) truncated Toeplitz operators are generally not complex symmetric. In this paper, we define a new conjugation with unique properties and study its relation to matrix valued asymmetric truncated Toeplitz operators. We also explore the connections between matrix valued asymmetric truncated Toep…

Matrix valued (asymmetric) truncated Toeplitz operators are generally not complex symmetric. In this paper, we define a new conjugation with unique properties and study its relation to matrix valued asymmetric truncated Toeplitz operators. We also explore the connections between matrix valued asymmetric truncated Toep…

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Bu çalışmada, q-tamsayılar temel alınarak tanımlanmış genelleştirilmiş bir Chlodowsky tipi Favard-Szász operatörü sunulmuştur. Bu operatörlerin ağırlıklı istatistiksel yaklaşım özellikleri incelenmiş ve davranışları Korovkin tipi yaklaşım teoremi kullanılarak değerlendirilmiştir. Ayrıca, yakınsama hızları, süreklilik…

This study presents a matrix-algebraic framework for deriving weighted Fibonacci identities from the $4 \times 4$ matrix $S_4^n(F_s, F_{s+1})$. By matching the closed-form entries of this matrix with the corresponding binomial expansions obtained from basis decomposition and structural convolution kernels, a new class…