A modified Gauss-type Proximal Point Algorithm (modified GG-PPA) is presented in this paper for solving the generalized equations like 0 ∈ T(x), where T a set-valued mapping acts between two different Banach spaces X and Y. By considering some necessary assumptions, we show existence of any sequence generated by GG-PPA prove semi-local local convergence results using metrically regular mapping....

In this paper, we propose a new second order numerical scheme for solving backward stochastic differential equations with jumps with the generator ( ) ( ) ( ) t t t t f r t x y h t z g t , , = + + Γ linearly depending on t z . And we theoretically prove that the convergence rates of them are of second order for solving t y and of first order for solving t z and t Γ in p L norm.

Convergence problems in coupled-cluster iterations are discussed, and a new iteration scheme is proposed. Whereas the Jacobi method inverts only the diagonal part of the large matrix of equation coefficients, we invert a matrix which also includes a relatively small number of off-diagonal coefficients, selected according to the excitation amplitudes undergoing the largest change in the coupled ...

We first study the fast minimization properties of the trajectories of the second-order evolution equation ẍ(t) + α t ẋ(t) + β∇Φ(x(t))ẋ(t) +∇Φ(x(t)) = 0, where Φ : H → R is a smooth convex function acting on a real Hilbert space H, and α, β are positive parameters. This inertial system combines an isotropic viscous damping which vanishes asymptotically, and a geometrical Hessian driven damping,...

the aim of this paper is to introduce and study a new concept of strong double δ ( a ) σ -convergence sequences with respect to an orlicz function, and some properties of the resulting sequencespaces were also examined. in addition, we define the δ ( a ) σ -statistical convergence and establish someconnections between the spaces of strong double δ ( a ) σ -convergence sequences and the space of...

Yu He Dept. of Physics Ohio State Univ. Columbus, OH 43212 We have calculated, both analytically and in simulations, the rate of convergence at long times in the backpropagation learning algorithm for networks with and without hidden units. Our basic finding for units using the standard sigmoid transfer function is lit convergence of the error for large t, with at most logarithmic corrections f...

In this paper, we design a novel alternating update method for solving a class of generalized bilinear programming problem, where each subproblem is regularized by a positive-definite proximal term to guarantee the convergence of the method. By using the tool of the variational inequality and the property of a monotonicity operator, its global convergence is analyzed and a worst-case O(1/t) con...

the concept of ${mathscr{f}}_{st}$-fundamentality is introduced in uniform spaces, generated by some filter ${mathscr{f}}$. its equivalence to the concept of ${mathscr{f}}$-convergence in uniform spaces is proved. this convergence generalizes many kinds of convergence, including the well-known statistical convergence.

The thermal discrete dipole approximation (T-DDA) is a numerical approach for modeling near-field radiative heat transfer in complex three-dimensional geometries. In this work, the convergence of the T-DDA is investigated by comparison against the exact results for two spheres separated by a vacuum gap. The error associated with the T-DDA is reported for various sphere sizes, refractive indices...

For the reference triangle or tetrahedron T , we study the stability properties of the L2(T )-projection ΠN onto the space of polynomials of degree N . We show ‖ΠNu‖L2(∂T ) ≤ C‖u‖L2(T )‖u‖H1(T ) and ‖ΠNu‖H1(T ) ≤ C(N + 1)‖u‖H1(T ). This implies optimal convergence rates for the approximation error ‖u−ΠNuu‖L2(∂T ) for all u ∈ Hk(T ), k > 1/2.