Results 41 to 50 of about 60,735 (247)
Continued fractions and periodic jacobi matrices
Linear Algebra and its Applications, 1992 The inverse eigenvalue problem for periodic Jacobi matrices is solved. Theoretical theorems on existence for different data are given and some algorithms (based on a continued fraction expansion) for solving this problem are described.
Andrea, Stephen A., Berry, T.G.
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Reconstructing Jacobi Matrices from Three Spectra [PDF]
, 2004 Cut a Jacobi matrix into two pieces by removing the n-th column and n-th row. We give neccessary and sufficient conditions for the spectra of the original matrix plus the spectra of the two submatrices to uniqely determine the original matrix. Our result contains Hostadt's original result as a special case.
Michor, Johanna, Teschl, Gerald
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On bounded complex Jacobi matrices and related moment problems in the complex plane [PDF]
Surveys in Mathematics and its Applications, 2023 In this paper we consider the following moment problem: find a positive Borel measure μ on ℂ subject to conditions ∫ zn dμ = sn, n∈ℤ+, where sn are prescribed complex numbers (moments).
Sergey M. Zagorodnyuk
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Darboux transformation of symmetric Jacobi matrices and Toda lattices
Frontiers in Applied Mathematics and StatisticsLet J be a symmetric Jacobi matrix associated with some Toda lattice. We find conditions for Jacobi matrix J to admit factorization J = LU (or J = 𝔘𝔏) with L (or 𝔏) and U (or 𝔘) being lower and upper triangular two-diagonal matrices, respectively.
Ivan Kovalyov, Oleksandra Levina
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Performance Comparison of GPU-Based Jacobi Solvers Using CUDA Provided Synchronization Methods
IEEE Access, 2020 In this manuscript, variants of Jacobi solver implementation on general purpose graphical processing units (GPGPU) have been purposed and compared. During this work, parallel implementation of finite element method (FEM) using Poisson's equation on ...
Maria Aslam +3 more
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CMV matrices in random matrix theory and integrable systems: a survey
, 2005 We present a survey of recent results concerning a remarkable class of unitary matrices, the CMV matrices. We are particularly interested in the role they play in the theory of random matrices and integrable systems.
Ammar G S +21 more
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Jacobi matrices with lacunary spectrum [PDF]
Journal of Mathematical Analysis and Applications, 2021 We find asymptotics of entries of Jacobi matrices with lacunary spectral data under some additional growth conditions. We also prove the inverse results. In addition, we study connections between Jacobi matrices, canonical systems and de Branges spaces for lacunary spectral ...
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On the Fourier expansions of Jacobi forms
International Journal of Mathematics and Mathematical Sciences, 2004 We use the relationship between Jacobi forms and vector-valued modular forms to study the Fourier expansions of Jacobi forms of indexes p, p2, and pq for distinct odd primes p, q.
Howard Skogman
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Journal of Computational and Applied Mathematics, 2001 This paper surveys and extends recent work on the connections between formal orthogonal polynomials, complex Jacobi continued fractions (\(J\)-fractions) and spectral properties of the underlying infinite complex symmetric tridiagonal (Jacobi) matrix. Special emphasis is given to unbounded recurrence coefficients.
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Finite gap Jacobi matrices: An announcement
Journal of Computational and Applied Mathematics, 2009 17 pages, 2 ...
Christiansen, Jacob S. +2 more
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