A calculus of symbols and convolution semigroups on the Heisenberg group
A class of pseudo differential operators with multiple non-involutive characteristics
A comparison of some efficient numerical methods for a nonlinear elliptic problem
The aim of this paper is to compare and realize three efficient iterative methods, which have mesh independent convergence, and to propose some improvements for them. We look for the numerical solution of a nonlinear model problem using FEM discretization with gradient and Newton type methods. Three numerical methods have been carried out, namely, the gradient, Newton and quasi-Newton methods. We have solved the model problem with these methods, we have investigated the differences between them...
A contribution to solving a system of two non-linear equations
A contribution to solving a system of two non-linear equations
A dual-parameter double-step splitting iteration method for solving complex symmetric linear equations
We multiply both sides of the complex symmetric linear system by to obtain a new equivalent linear system, then a dual-parameter double-step splitting (DDSS) method is established for solving the new linear system. In addition, we present an upper bound for the spectral radius of iteration matrix of the DDSS method and obtain its quasi-optimal parameter. Theoretical analyses demonstrate that the new method is convergent when some conditions are satisfied. Some tested examples are given to illustrate...
A finite element solution of the monlinear heat equation
A fixed point method to compute solvents of matrix polynomials
Matrix polynomials play an important role in the theory of matrix differential equations. We develop a fixed point method to compute solutions of matrix polynomials equations, where the matricial elements of the matrix polynomial are considered separately as complex polynomials. Numerical examples illustrate the method presented.
A frequency decomposition waveform relaxation algorithm for semilinear evolution equations.
A functional calculus for Rockland operators on nilpotent Lie groups
A Kantorovich-type Convergence Analysis for the Gauss-Newton-Method.
A method for obtaining iterative formulas of higer order
A new Variant of an Iterative Method for Solving the Complete Eigenvalue of Matrices
A Newton-Kantorovich-SOR type theorem
In this paper we propose a new method for solving nonlinear systems of equations in finite dimensional spaces, combining the Newton-Raphson's method with the SOR idea. For the proof we adapt Kantorovich's demonstration given for the Newton-Raphson's method. As applications we reobtain the classical Newton-Raphson's method and the author's Newton-Kantorovich-Seidel type result.
A note on direct methods for approximations of sparse Hessian matrices
Necessity of computing large sparse Hessian matrices gave birth to many methods for their effective approximation by differences of gradients. We adopt the so-called direct methods for this problem that we faced when developing programs for nonlinear optimization. A new approach used in the frame of symmetric sequential coloring is described. Numerical results illustrate the differences between this method and the popular Powell-Toint method.
A parallel projection method for linear algebraic systems
A direct projection method for solving systems of linear algebraic equations is described. The algorithm is equivalent to the algorithm for minimization of the corresponding quadratic function and can be generalized for the minimization of a strictly convex function.
A parametrized Newton method for nonsmooth equations with finitely many maximum functions
In this paper we propose a parametrized Newton method for nonsmooth equations with finitely many maximum functions. The convergence result of this method is proved and numerical experiments are listed.
A power series method for computing singular solutions to nonlinear analytic systems.
A projected Hessian Gauss-Newton algorithm for solving systems of nonlinear equations and inequalities.
A Rapid Generalized Method of Bisection for Solving Systems of Non-linear Equations.