A Generalized Projection method for systems of nonlinear equations " (1971). Retrospective Theses and Dissertations. Paper 4896. 1971 Signature was redacted for privacy. In this work a Projection method for solving systems of linear equations is extended to cover the nonlinear case. Projection methods fall into the broad class of minimization methods, which includes the various types of gradien...

We analyze pressure stabilized finite element methods for the solution of the generalized Stokes problem and investigate their stability and convergence properties. An important feature of the method is that the pressure gradient unknowns can be eliminated locally thus leading to a decoupled system of equations. Although stability of the method has been established, for the homogeneous Stokes e...

In this paper, we introduce an iterative sequence by using a hybrid generalized f−projection algorithm for finding a common element of the set of fixed points of a relatively weak nonexpansive mapping and the set of solutions of a generalized variational inequality in a Banach space. Our results extend and improve the recent ones announced by Y. Liu [Strong convergence theorems for variational ...

The convergence of the generalized alternating projection (GAP) algorithm is studied in this paper to solve the compressive sensing problem y = Ax + . By assuming that AA> is invertible, we prove that GAP converges linearly within a certain range of step-size when the sensing matrix A satisfies restricted isometry property (RIP) condition of δ2K , where K is the sparsity of x. The theoretical a...

and Applied Analysis 3 nonexpansive mapping such that F S ∩ A−10/ ∅. Let {xn} be a sequence generated by x0 x ∈ C and un J−1 ( βnJxn ( 1 − βn ) JSJrnxn ) , Cn { z ∈ C : φ z, un ≤ φ z, xn } , Qn {z ∈ C : 〈xn − z, Jx0 − Jxn〉 ≥ 0}, xn 1 ΠCn∩Qnx0 1.6 for all n ∈ N ∪ {0}, where J is the duality mapping on E, {βn} ⊂ 0, 1 , and {rn} ⊂ a,∞ for some a > 0. If lim infn→∞ 1 − βn > 0, then {xn} converges s...

A Bayesian approach to variable selection which is based on the expected Kullback–Leibler divergence between the full model and its projection onto a submodel has recently been suggested in the literature. For generalized linear models an extension of this idea is proposed by considering projections onto subspaces defined via some form of L1 constraint on the parameter in the full model. This l...

This paper focuses on Clarke generalized Jacobian of the projection onto symmetric cones. First, we recall some basic concepts. Let ̥ : Ω ⊆ X → Y be a locally Lipschitz function on an open set Ω, where X and Y are two finite dimensional inner product spaces over the field R. Let ∇̥(x) denote the derivative of ̥ at x if ̥ is differentiable at x. The Clarke generalized Jacobian of ̥ at x is defined by...

In this paper, we consider a new class of generalized variational inequalities and a new class of generalized Wiener-Hopf equations involving set-valued and nonexpansive mappings in real Hilbert space. Using the projection technique, we show that the generalized variational inequalities are equivalent to the generalized Wiener-Hopf equations. Further, by using this alternative equivalence we su...

This paper deals with systems of parametric equations over the reals, in the framework of interval constraint programming. As parameters vary within intervals, the solution set of a problem may have a non null volume. In these cases, an inner box (i.e., a box included in the solution set) instead of a single punctual solution is of particular interest, because it gives greater freedom for choos...

Improved phase space projection methods, adapted from related work in the linear signal processing field based on subspace decomposition, are presented for application to the problem of additive noise reduction in the context of phase space analysis. These methods improve upon existing methods such as Broomhead–King singular spectrum analysis projection by minimizing overall signal distortion s...