On a Three-Step Method with the Order of Convergence 1 + 2$$ \sqrt{2} $$ for the Solution of Systems of Nonlinear Operator Equations
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DOI: 10.1007/s10958-017-3279-6
Abstract: We propose a three-step modification of a method with an order of convergence 1+ 2$$ \sqrt{2} $$ aimed at the solution of nonlinear operator equations. We prove that the method is convergent and estimate its… read more here.
Keywords: three step; order convergence; operator equations; nonlinear operator ... See more keywords
System of multivariate pseudo-contractive operator equations and the existence of solutions
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DOI: 10.1007/s11784-018-0535-4
Abstract: The purpose of this paper is to study the following system of nonlinear operator equations for N-variable pseudo-contractive mappings $$T_1, T_2,\ldots ,T_N$$T1,T2,…,TN in a Banach space: $$\begin{aligned} {\left\{ \begin{array}{ll} T_1(x_{1},x_{2},\ldots ,x_{N})=x_1,\\ T_2(x_{1},x_{2},\ldots ,x_{N})=x_2,\\ T_3(x_{1},x_{2},\ldots ,x_{N})=x_3,\\… read more here.
Keywords: pseudo contractive; system; product banach; operator equations ... See more keywords
Singular Lyapunov operator equations: applications to $$C^*-$$algebras, Fréchet derivatives and abstract Cauchy problems
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DOI: 10.1007/s13324-021-00596-z
Abstract: Let A be a closed operator on a separable Hilbert space $$\mathcal {H}$$ . In this paper we obtain sufficient conditions for the existence of a solution to the Lyapunov operator equation $$ A^*X+X^*A=I$$ ,… read more here.
Keywords: singular lyapunov; operator equations; lyapunov operator; operator ... See more keywords
Convergence analysis of LSQR for compact operator equations
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DOI: 10.1016/j.laa.2019.08.024
Abstract: Abstract In this paper we analyze the behavior of the LSQR algorithm for the solution of compact operator equations in Hilbert spaces. We present results concerning existence of Krylov solutions and the rate of convergence… read more here.
Keywords: compact operator; lsqr; convergence; operator equations ... See more keywords
An open mapping theorem for nonlinear operator equations associated with elliptic complexes
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DOI: 10.1080/00036811.2021.2021190
Abstract: Let {A, E} be the elliptic complex on a n-dimensional smooth closed Riemannian manifold X with the first order differential operators A and smooth vector bundles E over X. We consider nonlinear operator equations, associated… read more here.
Keywords: order; nonlinear operator; differential operators; equations associated ... See more keywords
Direct and Converse Theorems for Iterative Methods of Solving Irregular Operator Equations and Finite Difference Methods for Solving Ill-Posed Cauchy Problems
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DOI: 10.1134/s0965542520060020
Abstract: Results obtained in recent years concerning necessary and sufficient conditions for the convergence (at a given rate) of approximation methods for solutions of irregular operator equations are overviewed. The exposition is given in the context… read more here.
Keywords: posed cauchy; cauchy problems; ill posed; operator equations ... See more keywords
Controllability and Optimal Controllability for Operator Equations of the First Kind in (B)-Spaces: Examples for ODE in $${{\mathbb{R}}^{n}}$$
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DOI: 10.1134/s1064562419020091
Abstract: For control and observation problems considered for operator equations of the first kind in Banach spaces, an controllability criterion is stated. In the case of reflexive strictly convex (B)-spaces, the BUME method and the method… read more here.
Keywords: controllability; first kind; operator equations; equations first ... See more keywords