Related papers: Application of the iterative approach to modal met…
Multiple scattering methods are widely used to reduce the computational complexity of acoustic or electromagnetic scattering problems when waves propagate through media containing many identical inclusions. Historically, this numerical…
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).…
In the aim of reducing the computational cost of the resolution of parameter-dependent eigenvalue problems, a model order reduction (MOR) procedure is proposed. We focus on the case of non-self-adjoint generalized eigenvalue problems, such…
This paper compares two basic approaches to solving ordinary differential equations, which form the basis for attitude computation in strapdown inertial navigation systems, namely, the Taylor series expansion approach that was used in its…
This work proposes a higher-order iterative framework for solving matrix equations, inspired by the structure and functionality of neural networks. A modification of the classical Jacobi iterative method is introduced to compute…
The numerical computation of the exponentiation of a real matrix has been intensively studied. The main objective of a good numerical method is to deal with round-off errors and computational cost. The situation is more complicated when…
Iterative methods based on tensors have emerged as powerful tools for solving tensor equations, and have significantly advanced across multiple disciplines. In this study, we propose two-step tensor-based iterative methods to solve the…
Iterative solutions of sparse linear systems and sparse eigenvalue problems have a fundamental role in vital fields of scientific research and engineering. The crucial computing kernel for such iterative solutions is the multiplication of a…
We study Bayesian methods for large-scale linear inverse problems, focusing on the challenging task of hyperparameter estimation. Typical hierarchical Bayesian formulations that follow a Markov Chain Monte Carlo approach are possible for…
This paper introduces a simple variant of the power method. It is shown analytically and numerically to accelerate convergence to the dominant eigenvalue/eigenvector pair; and, it is particularly effective for problems featuring a small…
Inverse iteration is known to be an effective method for computing eigenvectors corresponding to simple and well-separated eigenvalues. In the non-symmetric case, the solution of shifted Hessenberg systems is a central step. Existing…
This paper studies the iteration-complexity of new regularized hybrid proximal extragradient (HPE)-type methods for solving monotone inclusion problems (MIPs). The new (regularized HPE-type) methods essentially consist of instances of the…
A polyhedral method to solve a system of polynomial equations exploits its sparse structure via the Newton polytopes of the polynomials. We propose a hybrid symbolic-numeric method to compute a Puiseux series expansion for every space curve…
Complex valued systems with an indefinite matrix term arise in important applications such as for certain time-harmonic partial differential equations such as the Maxwell's equation and for the Helmholtz equation. Complex systems with…
A new iterative technique is presented for solving of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations. Proposed iterative scheme does not require any discretization,…
In earlier work we have studied a method for discretization in time of a parabolic problem which consists in representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In…
In this paper, we present a novel method to compute an explicit formula for the inverse of the confluent Vandermonde matrices. Our proposed results may have many interesting perspectives in diverse areas of mathematics and natural sciences,…
Some iterative techniques are defined to solve reversible inverse problems and a common formulation is explained. Numerical improvements are suggested and tests validate the methods.
In this paper we present a methodology for increasing the accuracy and accelerating the convergence of numerical methods for solution of Maxwell's equations in the frequency domain by taking into account the be-havior of the electromagnetic…
In this paper, we study first-order methods on a large variety of low-rank matrix optimization problems, whose solutions only live in a low dimensional eigenspace. Traditional first-order methods depend on the eigenvalue decomposition at…