In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm ineq...In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm inequalities for combination of orthogonal projections on a Hilbert space.Furthermore,we give necessary and sufficient conditions under which the norm of the above combination of o`rthogonal projections attains its optimal value.展开更多
Block boundary value methods(BBVMs)are extended in this paper to obtain the numerical solutions of nonlinear delay-differential-algebraic equations with singular perturbation(DDAESP).It is proved that the extended BBV...Block boundary value methods(BBVMs)are extended in this paper to obtain the numerical solutions of nonlinear delay-differential-algebraic equations with singular perturbation(DDAESP).It is proved that the extended BBVMs in some suitable conditions are globally stable and can obtain a unique exact solution of the DDAESP.Besides,whenever the classic Lipschitz conditions are satisfied,the extended BBVMs are preconsistent and pth order consistent.Moreover,through some numerical examples,the correctness of the theoretical results and computational validity of the extended BBVMs is further confirmed.展开更多
文摘In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm inequalities for combination of orthogonal projections on a Hilbert space.Furthermore,we give necessary and sufficient conditions under which the norm of the above combination of o`rthogonal projections attains its optimal value.
基金supported by the National Key R&D Program of China(2020YFA0709800)the National Natural Science Foundation of China(Nos.11901577,11971481,12071481,12001539)+4 种基金the Natural Science Foundation of Hunan(No.S2017JJQNJJ-0764)the fund from Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering(No.2018MMAEZD004)the Basic Research Foundation of National Numerical Wind Tunnel Project(No.NNW2018-ZT4A08)the Research Fund of National University of Defense Technology(No.ZK19-37)The science and technology innovation Program of Hunan Province(No.2020RC2039).
文摘Block boundary value methods(BBVMs)are extended in this paper to obtain the numerical solutions of nonlinear delay-differential-algebraic equations with singular perturbation(DDAESP).It is proved that the extended BBVMs in some suitable conditions are globally stable and can obtain a unique exact solution of the DDAESP.Besides,whenever the classic Lipschitz conditions are satisfied,the extended BBVMs are preconsistent and pth order consistent.Moreover,through some numerical examples,the correctness of the theoretical results and computational validity of the extended BBVMs is further confirmed.
