A Conjugate Gradient Method and a Multigrid Algorithm for Morley' s Finite Element Approximation of the Biharmonic Equation.
A conjugate gradient method with quasi-Newton approximation
The conjugate gradient method of Liu and Storey is an efficient minimization algorithm which uses second derivatives information, without saving matrices, by finite difference approximation. It is shown that the finite difference scheme can be removed by using a quasi-Newton approximation for computing a search direction, without loss of convergence. A conjugate gradient method based on BFGS approximation is proposed and compared with existing methods of the same class.
A conjugate gradient method with sufficient descent and global convergence for unconstrained nonlinear optimization.
A conservative finite difference scheme for static diffusion equation.
A conservative particle approximation for a boundary advection-diffusion problem
A conservative spectral element method for the approximation of compressible fluid flow
A method to approximate the Euler equations is presented. The method is a multi-domain approximation, and a variational form of the Euler equations is found by making use of the divergence theorem. The method is similar to that of the Discontinuous-Galerkin method of Cockburn and Shu, but the implementation is constructed through a spectral, multi-domain approach. The method is introduced and is shown to be a conservative scheme. A numerical example is given for the expanding flow around a point...
A Constant Space Representation of Digital Cubic Parabolas
A Constraint Linearization Method for Nondifferentiable Convex Minimization.
A Construction of Monotonically Convergent Sequences from Successive Approximations in Certain Banach Spaces.
A Constructive Method for Deriving Finite Elements of Nodal Type.
A Constructive Method of Solving the Liapounov Equation for Complex Matrices.
A continuous finite element method with face penalty to approximate Friedrichs' systems
A continuous finite element method to approximate Friedrichs' systems is proposed and analyzed. Stability is achieved by penalizing the jumps across mesh interfaces of the normal derivative of some components of the discrete solution. The convergence analysis leads to optimal convergence rates in the graph norm and suboptimal of order ½ convergence rates in the L2-norm. A variant of the method specialized to Friedrichs' systems associated with elliptic PDE's in mixed form and reducing the number...
A Continuous Selection of the Metric Projection in Matrix Spaces, Addendum.
A Contour Integral Representation of Linear Extrapolation Methods.
A contribution to Balas' algorithm
A contribution to Collatz's eigenvalue inclusion theorem for nonnegative irreducible matrices.
A contribution to Runge-Kutta formulas of the 7th order with rational coefficients for systems of differential equations of the first order
The purpose of this article is to find the 7th order formulas with rational parameters. The formulas are of the 11th stage. If we compare the coefficients of the development up to with the development given by successive insertion into the formula for and we obtain a system of 59 condition equations with 65 unknowns (except, the 1st one, all equations are nonlinear). As the solution of this system we get the parameters of the 7th order Runge-Kutta formulas as rational numbers.
A contribution to solving a system of two non-linear equations
A contribution to solving a system of two non-linear equations
A contribution to the successive over-relaxation method