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- Charles Byrne
- 2003

Let T be a (possibly nonlinear) continuous operator on Hilbert space H. If, for some starting vector x, the orbit sequence {T k x, k = 0, 1,. . .} converges, then the limit z is a fixed point of T ; that is, T z = z. An operator N on a Hilbert space H is nonexpansive (ne) if, for each x and y in H, N x − N y x − y. Even when N has fixed points the orbit… (More)

- Charles Byrne
- 2002

Let C and Q be nonempty closed convex sets in R N and R M , respectively, and A an M by N real matrix. The split feasibility problem (SFP) is to find x ∈ C with Ax ∈ Q, if such x exist. An iterative method for solving the SFP, called the CQ algorithm, has the following iterative step: x k+1 = P C (x k + γ A T (P Q − I)Ax k), where γ ∈ (0, 2/L) with L the… (More)

- Charles Byrne
- 2008

The problem of minimizing a function f (x) : R J → R, subject to constraints on the vector variable x, occurs frequently in inverse problems. Even without constraints, finding a minimizer of f (x) may require iterative methods. We consider here a general class of iterative algorithms that find a solution to the constrained minimization problem as the limit… (More)

Problems in signal detection and image recovery can sometimes be formulated as a convex feasibility problem (CFP) of finding a vector in the intersection of a finite family of closed convex sets. Algorithms for this purpose typically employ orthogonal or generalized projections onto the individual convex sets. The simultaneous multiprojection algorithm of… (More)

The EM algorithm is not a single algorithm, but a framework for the design of iterative likelihood maximization methods for parameter estimation. Any algorithm based on the EM framework we refer to as an " EM algorithm ". Because there is no inclusive theory that applies to all EM algorithms, the subject is a work in progress, and we find it appropriate to… (More)

- Charles Byrne
- 2013

We consider the problem of maximizing a non-negative function f : Z → R, where Z is an arbitrary set. We assume that there is z * ∈ Z with f (z *) ≥ f (z), for all z ∈ Z. We assume that there is a non-negative function b : R N × Z → R such that f (z) = b(x, z)dx. Having found z k , we maximize the function H(z k , z) = b(x, z k) log b(x, z)dx to get z k+1.… (More)

We introduce and study the Split Common Null Point Problem (SCNPP) for set-valued maximal monotone mappings in Hilbert spaces. The SCNPP with only two set-valued mappings entails finding a zero of a maximal monotone mapping in one space, the image of which 1 under a given bounded linear transformation is a zero of another maximal monotone mapping. We… (More)

- Charles Byrne, Charles Byrne@uml, Edu
- 2005

The recently presented sequential unconstrained minimization algorithm SUMMA is extended to provide a framework for the derivation of block-iterative, or partial-gradient, optimization methods. This BI-SUMMA includes, and is motivated by, block-iterative versions of the algebraic reconstruction technique (ART) and its multiplicative variant, the MART. The… (More)

OBJECTIVE
Little is known about the barriers, facilitators and interventions that impact on systematic review uptake. The objective of this study was to identify how uptake of systematic reviews can be improved.
SELECTION CRITERIA
Studies were included if they addressed interventions enhancing the uptake of systematic reviews. Reports in any language were… (More)

- Joe Qranfal, Charles Byrne, J Qranfal, C Byrne
- 2012

The new filtering algorithm EM (expectation maximization) filter is introduced and is validated numerically by applying it to solve the ill-posed inverse problem of reconstructing a time-varying medical image. A linear state-space stochastic approach based on a Markov process is utilized to model the problem, while no precise a-priori information about the… (More)