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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)
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)
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)
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)
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)
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)