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A Class of Preconditioners Based on positive-definite Operator Splitting Iteration Methods for Variable-Coefficient Space-Fractional Diffusion Equations

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Communications on Applied Mathematics and Computation 2021年第1期3卷 157-176页

作者： Jun-Feng Yin Yi-Shu Du School of Mathematical Sciences Tongji UniversityShanghai 200092China

After discretization by the finite volume method,the numerical solution of fractional diffusion equations leads to a linear system with the Toeplitz-like *** theoretical analysis gives sufficient conditions to guarantee the positive-definite property of the discretized ***,we develop a class of positive-definite operator splitting iteration methods for the numerical solution of fractional diffusion equations,which is unconditionally convergent for any positive ***,the iteration methods introduce a new preconditioner for Krylov subspace *** experiments verify the convergence of the positive-definite operator splitting iteration methods and show the efficiency of the proposed preconditioner,compared with the existing approaches.

关键词： Fractional diffusion equations Finite volume method Operator splitting positive-definite

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Stability of Operator-Valued Truncated Moment Problems

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Applied Mathematics 2013年第4期4卷 718-733页

作者： L. Lemnete-Ninulescu Department of Mathematics Politechnica University of Bucharest Bucharest Romania

In this note a multidimensional Hausdorff truncated operator-valued moment problem, from the point of view of “stability concept” of the number of atoms of the obtained atomic, operator-valued representing measure for the terms of a finite, positively define kernel of operators, is studied. The notion of “stability of the dimension” in truncated, scalar moment problems was introduced in [1]. In this note, the concept of “stability” of the algebraic dimension of the obtained Hilbert space from the space of the polynomials of finite, total degree with respect to the null subspace of a unital square positive functional, in [1], is adapted to the concept of stability of the algebraic dimension of the Hilbert space obtained as the separated space of some space of vectorial functions with respect to the null subspace of a hermitian square positive functional attached to a positive definite kernel of operators. In connection with the stability of the dimension of such obtained Hilbert space, a Hausdorff truncated operator-valued moment problem and the stability of the number of atoms of the representing measure for the terms of the given operator kernel, in this note, is studied.

关键词： Operator-Valued positive-definite Function Unitary-Operator Selfadjoint Operator Joint Spectral Measure of a Commuting Tuple of Operators Atomic Measure Extension of Some Hermitian Square positive Functional

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