相关论文: A Fast Solver for Tridiagonal Toeplitz Systems wit…
Transcatheter valve repair presents significant challenges due to the mechanical limitations and steep learning curve associated with manual catheter systems. This paper investigates the use of robotics to facilitate transcatheter…
This paper proposes an explicit computational method for solving a three-dimensional system of nonlinear elastodynamic sine-Gordon equations subject to appropriate initial and boundary conditions. The time derivative is approximated by…
We present new approaches for solving constrained multicomponent nonlinear Schr\"odinger equations in arbitrary dimensions. The idea is to introduce an artificial time and solve an extended damped second order dynamic system whose…
A parallel fast direct solver for rank-compressible block tridiagonal linear systems is presented. Algorithmic synergies between Cyclic Reduction and Hierarchical matrix arithmetic operations result in a solver with $O(N \log^2 N)$…
A new approach to problems of the Uncertainty Principle in Harmonic Analysis, based on the use of Toeplitz operators, has brought progress to some of the classical problems in the area. The goal of this paper is to develop and systematize…
This paper addresses multilinear systems of equations which arise in various applications such as data mining and numerical partial differential equations. When the multilinear system under consideration involves a nonsingular…
Various versions of the Dynamical Systems Method (DSM) are proposed for solving linear ill-posed problems with bounded and unbounded operators. Convergence of the proposed methods is proved. Some new results concerning discrepancy principle…
The integration of multi-view imaging and pose estimation represents a significant advance in computer vision applications, offering new possibilities for understanding human movement and interactions. This work presents a new algorithm…
In this paper we define a small variation of the Taylor method and a formula for the global error of this new numerical method that allows us to keep track of the round-off error and does not require previous knowledge of the exact…
Regularity properties of strong solutions are considered.
We propose a third order dynamical system for solving a nonlinear equation in Hilbert spaces where the operator is cocoercive with respect to the solutions set. Under mild conditions on the parameters, we establish the existence and…
Multi-soliton solution of the 3-waves problem is represented in explicit determinative form.
This paper focuses on the resolution of infinite-dimensional Toeplitz Block LMIs, which are frequently encountered in the context of stability analysis and control design problems formulated in the harmonic framework. We propose a…
The paper proposes a novel hybrid method for solving equilibrium problems and fixed point problems. By constructing specially cutting-halfspaces, in this algorithm, only an optimization program is solved at each iteration without the…
We present an asymptotically faster algorithm for solving linear systems in well-structured 3-dimensional truss stiffness matrices. These linear systems arise from linear elasticity problems, and can be viewed as extensions of graph…
New solution method for the systems of linear equations in commutative integral domains is proposed. Its complexity is the same that the complexity of the matrix multiplication.
Two new approaches to solving first-order quasilinear elliptic systems of PDEs in many dimensions are proposed. The first method is based on an analysis of multimode solutions expressible in terms of Riemann invariants, based on links…
An existing solvability result for relaxed one-sided Lipschitz algebraic inclusions is substantially improved. This enhanced solvability result allows the design of a very robust numerical method for the approximation of a solution of the…
By setting up appropriate uniform convergence structures, we are able to reformulate the Order Completion Method of Oberguggenberger and Rosinger in a setting that more closely resembles the usual topological constructions for solving PDEs.…
We use the "tridiagonal representation approach" to solve the time-independent Schr\"odinger equation for the bound states of generalized versions of the trigonometric and hyperbolic P\"oschl-Teller potentials. These new solvable potentials…