相关论文: An iterative method to solve Lyapunov equations
The solution of systems of linear(ized) equations lies at the heart of many problems in Scientific Computing. In particular for systems of large dimension, iterative methods are a primary approach. Stationary iterative methods are generally…
In this work we discuss the possibility to reduce the computational complexity of modal methods, i.e. methods based on eigenmodes expansion, from the third power to the second power of the number of eigenmodes. The proposed approach is…
We established a new eighth-order iterative method, consisting of three steps, for solving nonlinear equations. Per iteration the method requires four evaluations (three function evaluations and one evaluation of the first derivative).…
The new class of alternating-conjugate splitting methods is presented and analyzed. They are obtained by concatenating a given composition involving complex coefficients with the same composition but with the complex conjugate coefficients.…
Efficiently solving sparse linear algebraic equations is an important research topic of numerical simulation. Commonly used approaches include direct methods and iterative methods. Compared with the direct methods, the iterative methods…
Splitting methods are widely used for solving initial value problems (IVPs) due to their ability to simplify complicated evolutions into more manageable subproblems which can be solved efficiently and accurately. Traditionally, these…
New iterative methods for solving linear equations are presented that are easy to use, generalize good existing methods, and appear to be faster. The new algorithms mix two kinds of linear recurrence formulas. Older methods have either high…
In a previous work, we developed the idea to solve Kepler's equation with a CORDIC-like algorithm, which does not require any division, but still multiplications in each iteration. Here we overcome this major shortcoming and solve Kepler's…
The Baxter-Bazhanov-Stroganov model (also known as the \tau^(2) model) has attracted much interest because it provides a tool for solving the integrable chiral Z_N-Potts model. It can be formulated as a face spin model or via cyclic…
Computing the regularized solution of Bayesian linear inverse problems as well as the corresponding regularization parameter is highly desirable in many applications. This paper proposes a novel iterative method, termed the Projected Newton…
We apply mixed-precision to the low-rank Lyapunov ADI (LR-ADI) by performing certain aspects of the algorithm in a lower working precision. Namely, we accumulate the overall solution, solve the linear systems comprising the ADI iteration,…
This paper proposes and establishes the iteration-complexity of an inexact proximal accelerated augmented Lagrangian (IPAAL) method for solving linearly constrained smooth nonconvex composite optimization problems. Each IPAAL iteration…
In recent years, accelerated extra-gradient methods have attracted much attention by researchers, for solving monotone inclusion problems. A limitation of most current accelerated extra-gradient methods lies in their direct utilization of…
We consider linear ill-conditioned operator equations in a Hilbert space setting. Motivated by the aggregation method, we consider approximate solutions constructed from linear combinations of Tikhonov regularization, which amounts to…
One of the most computationally expensive steps of the low-rank ADI method for large-scale Lyapunov equations is the solution of a shifted linear system at each iteration. We propose the use of the extended Krylov subspace method for this…
A new version of the alternating directions implicit (ADI) iteration for the solution of large-scale Lyapunov equations is introduced. It generalizes the hitherto existing iteration, by incorporating tangential directions in the way they…
Matrix splitting iteration methods play a vital role in solving large sparse linear systems. Their performance heavily depends on the splitting parameters, however, the approach of selecting optimal splitting parameters has not been well…
We propose an iterative finite element method for solving non-linear hydromagnetic and steady Euler's equations. Some three-dimensional computational tests are given to confirm the convergence and the high efficiency of the method.
Often in the study the periodic orbits in dynamical systems, the computation of the Lyapunov Coeficients is needed. In this paper, the calculations of this coeficients were done via complex variable transformation in order to obtain the…
We consider a boundary value problem involving a Riemann-Liouville fractional derivative of order $\alpha\in (3/2,2)$ on the unit interval $(0,1)$. The standard Galerkin finite element approximation converges slowly due to the presence of…