Robust stability of linear time-varying implicit dynamic equations: a general consideration

Thuan, Do Duc; Nguyen, Khong Chi; Hà, Nguyễn Thu; Du, Nguyen Huu

doi:10.1007/s00498-019-0242-8

Cited by 5 publications

(1 citation statement)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where matrix A is an n × n matrix and x and b are n-dimensional column vectors. Te methods for solving linear equations mainly include square root method, elimination method, direct triangular decomposition method, determinant and matrix inversion, Seidel iteration method, Jacobi iteration method, super relaxation iteration method, and other iteration methods [4].…”

Section: The Structure Preprocessing Methods For the System Of Unclos...mentioning

confidence: 99%

Structure Preprocessing Method for the System of Unclosed Linear Algebraic Equations

2022

Journal of Mathematics

View full text Add to dashboard Cite

The complexity of open linear algebraic equations makes it difficult to obtain analytical solutions, and preprocessing techniques can be applied to coefficient matrices, which has become an effective method to accelerate the convergence of iterative methods. Therefore, it is important to preprocess the structure of open linear algebraic equations to reduce their complexity. Open linear algebraic equations can be divided into symmetric linear equations and asymmetric linear equations. The former is based on 2 × 2. The latter is preprocessed by the improved QMRGCGS method, and the applications of the two methods are analyzed, respectively. The experimental results show that when the step is 500, the pretreatment time of quasi-minimal residual generalized conjugate gradient square 2 method is 34.23 s, that of conjugate gradient square 2 method is 35.14 s, and that of conjugate gradient square method is 45.20 s, providing a new reference method and idea for solving and preprocessing non-closed linear algebraic equations.

show abstract

Section: The Structure Preprocessing Methods For the System Of Unclos...mentioning

confidence: 99%

Structure Preprocessing Method for the System of Unclosed Linear Algebraic Equations

2022

Journal of Mathematics

View full text Add to dashboard Cite

show abstract

Stability radii of differential–algebraic equations with respect to stochastic perturbations

Thuan

Sơn

Tinh

2021

Systems & Control Letters

View full text Add to dashboard Cite

On the robust stability of Volterra differential–algebraic equations

Hà

2021

Systems & Control Letters

View full text Add to dashboard Cite

Robust stability of linear time-varying implicit dynamic equations: a general consideration

Cited by 5 publications

References 29 publications

Structure Preprocessing Method for the System of Unclosed Linear Algebraic Equations

Structure Preprocessing Method for the System of Unclosed Linear Algebraic Equations

Stability radii of differential–algebraic equations with respect to stochastic perturbations

On the robust stability of Volterra differential–algebraic equations

Contact Info

Product

Resources

About