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Stephen L. Keeling 《BIT Numerical Mathematics》1989,29(1):91-109
Because of their potential for offering a computational speed-up when used on certain multiprocessor computers, implicit Runge-Kutta methods with a stability function having distinct poles are analyzed. These are calledmultiply implicit (MIRK) methods, and because of the so-calledorder reduction phenomenon, their poles are required to be real, i.e., only real MIRK's are considered. Specifically, it is proved that a necessary condition for aq-stage, real MIRK to beA-stable with maximal orderq+1 is thatq=1, 2, 3 or 5. Nevertheless, it is shown that for every positive integerq, there exists aq-stage, real MIRK which is stronglyA
0-stable with orderq+1, and for every evenq, there is aq-stage, real MIRK which isI-stable with orderq. Finally, some useful examples of algebraically stable real MIRK's are given.This work was supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-18107 while the author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23665-5225. 相似文献
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A general theory of uniform approximation with rational functions having negative poles is developed. An existence theory is given and local characterization and uniqueness results are developed. Algorithms for computing these approximants are given, together with numerical results. 相似文献
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Michael Müller 《BIT Numerical Mathematics》1992,32(4):676-688
The implementation of implicit Runge-Kutta methods requires the solution of large sets of nonlinear equations. It is known that on serial machines these costs can be reduced if the stability function of ans-stage method has only ans-fold real pole. Here these so-called singly-implicit Runge-Kutta methods (SIRKs) are constructed utilizing a recent result on eigenvalue assignment by state feedback and a new tridiagonalization, which preserves the entries required by theW-transformation. These two algorithms in conjunction with an unconstrained minimization allow the numerical treatment of a difficult inverse eigenvalue problem. In particular we compute an 8-stage SIRK which is of order 8 andB-stable. This solves a problem posed by Hairer and Wanner a decade ago. Furthermore, we finds-stageB-stable SIRKs (s=6,8) of orders, which are evenL-stable. 相似文献
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Summary In this paper we consider Riemannian metrics without conjugate points on an n-torus. Recent work of J. Heber established that the gradient vector fields of Busemann functions on the universal cover of such a manifold induce a natural foliation (akin to the weak stable foliation for a Riemannian manifold with negative sectional curvature) on the unit tangent bundle. The main result in the paper is that the metric is flat if this foliation is Lipschitz. We also prove that this foliation is Lipschitz if and only if the metric has bounded asymptotes. This confirms a conjecture of E. Hopf in this case.Oblatum 22-IX-1993 & 25-IV-1994Supported in part by NSF grant #DMS90-01707 and #DMS85-05550 while at MSRISupported by an NSF Postdoctoral Fellowship 相似文献
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V. E. Voskresenskii 《Journal of Mathematical Sciences》2009,161(1):176-180
The faithful representations of quasisplit k-tori are studied. The old-standing conjecture of the rationality of stably rational tori is proved. Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 60, Algebra, 2008. 相似文献
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W. Hürlimann 《Commentarii Mathematici Helvetici》1984,59(1):539-549
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Otsuki tori in the three-dimensional unit sphere are studied. From calculations of the Willmore energy, the lower and upper bound estimates for the Otsuki tori are established. Invariance of the Otsuki tori under antipodal maps is also considered and, in such cases, better lower bound estimates of their Willmore energies are obtained. 相似文献
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It is shown that there exist A-stable multistep formulae, with a characteristic function havings poles, all of which are real, with orderp satisfyingp>s+1. This contradicts the widely held belief thatp=s+1 is the maximum possible order of such a method. 相似文献
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On elliptic lower dimensional tori in hamiltonian systems 总被引:13,自引:0,他引:13
Jürgen Pöschel 《Mathematische Zeitschrift》1989,202(4):559-608
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R. Pacheco 《Differential Geometry and its Applications》2009,27(3):352-361
In this paper we prove that, in contrast with the Sn and CPn cases, there are harmonic 2-tori into the quaternionic projective space HPn which are neither of finite type nor of finite uniton number; we also prove that any harmonic 2-torus in a compact Riemannian symmetric space which can be obtained via the twistor construction is of finite type if and only it is constant; in particular, we conclude that any harmonic 2-torus in CPn or Sn which is simultaneously of finite type and of finite uniton number must be constant. 相似文献