The solution of PDE-constrained optimal control problems is a computationally challenging task, and it involves the solution of structured algebraic linear systems whose blocks stem from the discretized first-order optimality conditions. In this paper we analyze the numerical solution of this...

Let Ω and C be nonempty, closed and convex sets in R <Superscript> n </Superscript> and R <Superscript> m </Superscript> respectively and A be an <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${m \times n}$$</EquationSource> </InlineEquation> real matrix. The split feasibility problem is to find <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${u \in \Omega}$$</EquationSource> </InlineEquation> with <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$${Au \in C.}$$</EquationSource> </InlineEquation> Many problems arising in the image reconstruction can be formulated in this form. In...</equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></superscript></superscript>

Sparsified Randomization Monte Carlo (SRMC) algorithms introduced in our recent paper [60] for solving systems of linear algebraic equations are extended to construct the SVD-based randomized low rank approximations for large matrices. We suggest some efficient implementations of SRMC based on...

Purpose – Multidimensional scaling (MDS) represents a family of various geometric models for the multidimensional representation of the structure in data as well as the corresponding set of methods for fitting such spatial models. Its major uses in business include positioning, market...

A competition which is based on the results of (partial) pairwise comparisons can be modelled by means of a directed graph.Given initial weights on the nodes in such digraph competitions, we view the measurement of the importance (i.e., the cardinal ranking) of the nodes as an allocation problem...

This paper presents an iterative alternating algorithm for solving an inverse problem in linear elasticity. A relaxation procedure is developed in order to increase the rate of convergence of the algorithm and two selection criteria for the variable relaxation factors are provided. The boundary...