Modified Douglas splitting method for differential matrix equations

2021 ◽  
Vol 384 ◽  
pp. 113162
Author(s):  
Hao Chen ◽  
Ying Wang
Keyword(s):  
Splitting Method ◽  
Matrix Equations ◽  
Differential Matrix

Calculation of the Natural Frequencies of Transverse Vibration of Complex Beams Using the Differential-Matrix Equations

2011 ◽  
Vol 243-249 ◽  
pp. 284-289
Author(s):  
Yu Zhang
Keyword(s):  
Iterative Method ◽  
Boundary Conditions ◽  
Cross Section ◽  
Transverse Vibration ◽  
Natural Frequencies ◽  
Composite Beams ◽  
Matrix Equations ◽  
Generalized Differential ◽  
Set Up ◽  
Differential Matrix

The generalized differential-matrix equations of transverse vibration of the beams were set up and they were solved by means of Cauchy sequence iterative method. Then according to the boundary conditions at two ends of the beams the natural frequencies of the transverse vibration of the different beams including the complex beams of non-uniform section and composite beams under different boundary conditions were figured out. The form of the differential-matrix is simple. The calculation of the sequence iterations can be accomplished by simple computer program. Using the method in this paper, the amount of work of calculation is reduced greatly and the results are accurate compared with the approximate method in which a beam of non-uniform section is replaced by many small segments of equal cross-section.

An LDLT factorization based ADI algorithm for solving large-scale differential matrix equations

PAMM ◽  
2014 ◽  
Vol 14 (1) ◽  
pp. 827-828 ◽  
Author(s):  
Norman Lang ◽  
Hermann Mena ◽  
Jens Saak
Keyword(s):  
Large Scale ◽  
Matrix Equations ◽  
Differential Matrix

scholarly journals GPU acceleration of splitting schemes applied to differential matrix equations

2019 ◽  
Vol 83 (1) ◽  
pp. 395-419
Author(s):  
Hermann Mena ◽  
Lena-Maria Pfurtscheller ◽  
Tony Stillfjord
Keyword(s):  
Gpu Acceleration ◽  
Matrix Equations ◽  
Splitting Schemes ◽  
Differential Matrix

scholarly journals Iterative Algorithms for Symmetric Positive Semidefinite Solutions of the Lyapunov Matrix Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-10 ◽  
Author(s):  
Min Sun ◽  
Jing Liu
Keyword(s):  
Splitting Method ◽  
Iterative Algorithms ◽  
Positive Semidefinite ◽  
Matrix Equations ◽  
Proximal Point ◽  
Alternating Direction ◽  
Lyapunov Matrix ◽  
Lyapunov Matrix Equations ◽  
The Stability ◽  
Constrained Solutions

It is well-known that the stability of a first-order autonomous system can be determined by testing the symmetric positive definite solutions of associated Lyapunov matrix equations. However, the research on the constrained solutions of the Lyapunov matrix equations is quite few. In this paper, we present three iterative algorithms for symmetric positive semidefinite solutions of the Lyapunov matrix equations. The first and second iterative algorithms are based on the relaxed proximal point algorithm (RPPA) and the Peaceman–Rachford splitting method (PRSM), respectively, and their global convergence can be ensured by corresponding results in the literature. The third iterative algorithm is based on the famous alternating direction method of multipliers (ADMM), and its convergence is subsequently discussed in detail. Finally, numerical simulation results illustrate the effectiveness of the proposed iterative algorithms.

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