Scalability of k-Tridiagonal Matrix Singular Value Decomposition

Tănăsescu, Andrei; Carabaș, Mihai; Pop, Florin; Popescu, Pantelimon George

doi:10.3390/math9233123

Cited by 5 publications

(4 citation statements)

References 28 publications

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“…The algorithm uses the fast block diagonalization method. Tanasescu A et al [21,22] proposed the singular value decomposition of a k-tridiagonal matrix that can be calculated in O(n 3 /k 2 ) and a technique for enhancing any existing SVD algorithm to make it suitable for this class of matrices. Da Fonseca CM et al [3,4] developed the spectral theory for k-tridiagonal matrices, which are the first type of matrices.…”

Section: Introductionmentioning

confidence: 99%

Symbolic Algorithm for Inverting General k-Tridiagonal Interval Matrices

Thirupathi

Thamaraiselvan²

2023

Int. J. Anal. Appl.

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The k-tridiagonal matrices have received much attention in recent years. Many different algorithms have been proposed to improve the efficiency of k-tridiagonal matrix estimation. A novel method based on interval analysis has been identified to improve the efficiency of the calculation. This paper presents efficient and reliable computational algorithms for determining the determinant and inverse of general k-tridiagonal interval matrices built on generalized interval arithmetic. This study is based on the Doolittle LU factorization of the interval matrix. Finally, examples are presented to illustrate the algorithms.

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Section: Introductionmentioning

confidence: 99%

Symbolic Algorithm for Inverting General k-Tridiagonal Interval Matrices

Thirupathi

Thamaraiselvan²

2023

Int. J. Anal. Appl.

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“…Matrix decomposition is to decompose a matrix into the product of several low rank or special structure matrices. There are many types of matrix decomposition which are widely used in scientific research and engineering applications [25][26][27][28][29][30][31][32][33][34][35]. For instance, a method for calculating polar decomposition is proposed in [27].…”

Section: Introductionmentioning

confidence: 99%

Continuous and Discrete ZND Models with Aid of Eleven Instants for Complex QR Decomposition of Time-Varying Matrices

Chen,

Kang,

Zhang

2023

Mathematics

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The problem of QR decomposition is considered one of the fundamental problems commonly encountered in both scientific research and engineering applications. In this paper, the QR decomposition for complex-valued time-varying matrices is analyzed and investigated. Specifically, by applying the zeroing neural dynamics (ZND) method, dimensional reduction method, equivalent transformations, Kronecker product, and vectorization techniques, a new continuous-time QR decomposition (CTQRD) model is derived and presented. Then, a novel eleven-instant Zhang et al discretization (ZeaD) formula, with fifth-order precision, is proposed and studied. Additionally, five discrete-time QR decomposition (DTQRD) models are further obtained by using the eleven-instant and other ZeaD formulas. Theoretical analysis and numerical experimental results confirmed the correctness and effectiveness of the proposed continuous and discrete ZND models.

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“…Thirupathi S et al [19] developed an algorithm based on generalized interval arithmetic to determine general k-tridiagonal interval matrix determinants and inverses. Tanasescu A et al [20,21] used the block diagonalization of a general k-tridiagonal matrix to study its singular value decomposition. Wei F et al [22] used the interval matrix technique to investigate the finite-time stability of memristor-based inertial neural networks (MINNs).…”

Section: Introductionmentioning

confidence: 99%

A Symbolic Algorithm for Solving Doubly Bordered k-Tridiagonal Interval Linear Systems

Thirupathi,

Thamaraiselvan

2023

Int. J. Anal. Appl.

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Doubly bordered k-tridiagonal interval linear systems play a crucial role in various mathematical and engineering applications where uncertainty is inherent in the system’s parameters. In this paper, we propose a novel symbolic algorithm for solving such systems efficiently. Our approach combines symbolic computation techniques with interval arithmetic to provide rigorous solutions in the form of tight interval enclosures. By exploiting the tridiagonal structure and employing a divide-and-conquer strategy, our algorithm achieves significantly reduced computational complexity compared to existing numerical methods. We also present theoretical analysis and provide numerical experiments to demonstrate the effectiveness and accuracy of our algorithm. The proposed symbolic algorithm offers a valuable tool for handling doubly bordered k-tridiagonal interval linear systems and opens up possibilities for addressing uncertainty in real-world problems with improved efficiency and reliability.

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Scalability of k-Tridiagonal Matrix Singular Value Decomposition

Cited by 5 publications

References 28 publications

Symbolic Algorithm for Inverting General k-Tridiagonal Interval Matrices

Symbolic Algorithm for Inverting General k-Tridiagonal Interval Matrices

Continuous and Discrete ZND Models with Aid of Eleven Instants for Complex QR Decomposition of Time-Varying Matrices

A Symbolic Algorithm for Solving Doubly Bordered k-Tridiagonal Interval Linear Systems

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