Results 1 to 10 of about 7,423,787 (281)

Simplification of the Gram Matrix Eigenvalue Problem for Quadrature Amplitude Modulation Signals [PDF]

Entropy, 2022
In quantum information science, it is very important to solve the eigenvalue problem of the Gram matrix for quantum signals. This allows various quantities to be calculated, such as the error probability, mutual information, channel capacity, and the ...
Ryusuke Miyazaki, Tiancheng Wang, Tsuyoshi Sasaki Usuda   +2 more
doaj   +2 more sources

A Test Matrix for an Inverse Eigenvalue Problem [PDF]

Journal of Applied Mathematics, 2014
We present a real symmetric tridiagonal matrix of order n whose eigenvalues are {2k}k=0n-1 which also satisfies the additional condition that its leading principle submatrix has a uniformly interlaced spectrum, {2l+1}l=0n-2.
G. M. L. Gladwell, T. H. Jones, N. B. Willms   +2 more
doaj   +6 more sources

Inverse Eigenvalue Problems for Two Special Acyclic Matrices

Mathematics, 2016
In this paper, we study two inverse eigenvalue problems (IEPs) of constructing two special acyclic matrices. The first problem involves the reconstruction of matrices whose graph is a path, from given information on one eigenvector of the required matrix
Debashish Sharma, Mausumi Sen
doaj   +3 more sources

Matrix Representations for a Class of Eigenparameter Dependent Sturm–Liouville Problems with Discontinuity

Axioms, 2023
Matrix representations for a class of Sturm–Liouville problems with eigenparameters contained in the boundary and interface conditions were studied. Given any matrix eigenvalue problem of a certain type and an eigenparameter-dependent condition, a class ...
Shuang Li, Jinming Cai, Kun Li
doaj   +1 more source

Efficient Reduction Algorithms for Banded Symmetric Generalized Eigenproblems via Sequentially Semiseparable (SSS) Matrices

Mathematics, 2022
In this paper, a novel algorithm is proposed for reducing a banded symmetric generalized eigenvalue problem to a banded symmetric standard eigenvalue problem, based on the sequentially semiseparable (SSS) matrix techniques.
Fan Yuan, Shengguo Li, Hao Jiang, Hongxia Wang, Cheng Chen, Lei Du, Bo Yang   +6 more
doaj   +1 more source

Analytical solutions to some generalized and polynomial eigenvalue problems

Special Matrices, 2021
It is well-known that the finite difference discretization of the Laplacian eigenvalue problem −Δu = λu leads to a matrix eigenvalue problem (EVP) Ax =λx where the matrix A is Toeplitz-plus-Hankel.
Deng Quanling
doaj   +1 more source

Calculation of Critical Load of Axially Functionally Graded and Variable Cross-Section Timoshenko Beams by Using Interpolating Matrix Method

Mathematics, 2022
In this paper, the interpolation matrix method (IMM) is proposed to solve the buckling critical load of axially functionally graded (FG) Timoshenko beams.
Renyu Ge, Feng Liu, Chao Wang, Liangliang Ma, Jinping Wang   +4 more
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A Note on NIEP for Leslie and Doubly Leslie Matrices

Mathematics, 2020
The nonnegative inverse eigenvalue problem (NIEP) consists of finding necessary and sufficient conditions for the existence of a nonnegative matrix with a given list of complex numbers as its spectrum.
Luis Medina, Hans Nina, Elvis Valero
doaj   +1 more source

Inverse spectral problem of a class of fourth-order eigenparameter-dependent boundary value problems

Advances in Difference Equations, 2020
This paper deals with a class of inverse spectral problems of fourth-order boundary value problems with eigenparameter-dependent boundary conditions.
Ji-jun Ao, Liang Zhang
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Two inverse eigenvalue problems for matrices whose graphs are trees

AKCE International Journal of Graphs and Combinatorics, 2023
Inverse eigenvalue problem refers to the problem of reconstructing a matrix of a desired structure from a prescribed eigendata. In this paper, we discuss two additive inverse eigenvalue problems for matrices whose graph is tree.
Bijoya Bardhan, Mausumi Sen, Debashish Sharma   +2 more
doaj   +1 more source