科学计算用数字电子计算机的若干问题

数字电子计算机的发明与发展的主要动力是大型科学计算.计算机是应科学计算的需要而发明的,应科学计算的不断追求而迅速发展的.科学计算课题的要求是无限的,而计算机的解题能力是有限的,装备计算机的技术也是有限的.因此如何处处“节约”技术,最“经济”地使用技术,以当前有限的技术研制出计算能力尽可能大的计算机是科学计算工作者很关心的问题.     

科学计算及其在晶体生长研究中的应用

本文阐述了科学计算的内容、方法和意义，讨论了科学计算在晶体生长研究中的作用以及对工科数学教学的启示。     

科学计算及其在晶体生长研究中的应用

本文阐述了科学计算的内容、方法和意义．讨论了科学计算在晶体生长研究中的作用以及对工科数学教学的启示．     

略论科学计算在理论研究中的作用

本文略述“科学计算”的内容、方法和意义,并通过两个特别引人注目的事例的介绍,着重阐述科学计算对理论研究的重大作用.     

“冯康科学计算奖”奖励条例

第一条 为纪念冯康先生对中国计算数学事业所做的杰出贡献,特设立“冯康科学计算奖” 奖励基金。第二条 本奖奖励在科学计算领域作出突出贡献的年龄在45岁以下(包括45岁)的海内外 中国青年科学家。     

科学计算软件和科学计算软件工程学

本文介绍了科学计算软件的内容及其重要性.以一些例子说明科学计算软件工程学的研究对象、内容和方法.提出了从事科技软件工作人员所应具有的知识结构.以上各点均为作者的一管之见,希望就这些问题就教于各位同行.     

“计算方法”教学的一个案例

“计算方法”是培养学生算法意识和能力的基本课程,不能靠单纯讲授来培养学生的科学计算能力,必须在计算机环境下通过实验来完成科学计算的综合训练．本文结合自己的教学实践,探讨在“计算方法”课程中应用数学软件MATLAB进行“曲线拟合”教学的一个案例．     

周毓麟先生在计算数学领域的成就与贡献——纪念周毓麟院士百年诞辰

本文从计算数学的视角,介绍周毓麟先生在离散泛函分析方法和大型科学计算方法等领域的研究工作.     

Mathematica数学软件的浮点数值精度问题

本文讨论了 Mathematica软件中的浮点计算精度问题 ,阐明了常量＄ Machine Epsilon的来历 ,有助于正确使用 Mathematica进行科学计算 .     

线性代数要与科学计算结成好伙伴

讨论了大学教学中科学计算能力的重要性,评价了我国在这个领域的落后状况.一是科学计算能力的培养无人主管;二是线性代数课程忽视实用性,不教矩阵软件,与后续课的需求及计算机脱节.这两者的长期割裂阻碍了我国课程和教育的现代化.文章提供的历史经验和国内外实践,都证明这两者的结合可以产生巨大的创新效果.文章结合十五年来的改革经验,提出改进的建议,并介绍了教育部"用MATLAB和建模实践改革工科线性代数"项目的实施情况.     

On a proper acute triangulation of a polyhedral surface

Let Σ be a polyhedral surface in R³ with n edges. Let L be the length of the longest edge in Σ, δ be the minimum value of the geodesic distance from a vertex to an edge that is not incident to the vertex, and θ be the measure of the smallest face angle in Σ. We prove that Σ can be triangulated into at most CLn/(δθ) planar and rectilinear acute triangles, where C is an absolute constant.     

Conforming Delaunay triangulations in 3D

We describe an algorithm which, for any piecewise linear complex (PLC) in 3D, builds a Delaunay triangulation conforming to this PLC. The algorithm has been implemented, and yields in practice a relatively small number of Steiner points due to the fact that it adapts to the local geometry of the PLC. It is, to our knowledge, the first practical algorithm devoted to this problem.     

Geodesic ideal triangulations exist virtually

It is shown that every non-compact hyperbolic manifold of finite volume has a finite cover admitting a geodesic ideal triangulation. Also, every hyperbolic manifold of finite volume with non-empty, totally geodesic boundary has a finite regular cover which has a geodesic partially truncated triangulation. The proofs use an extension of a result due to Long and Niblo concerning the separability of peripheral subgroups.

     

Manifold Reconstruction in Arbitrary Dimensions Using Witness Complexes

It is a well-established fact that the witness complex is closely related to the restricted Delaunay triangulation in low dimensions. Specifically, it has been proved that the witness complex coincides with the restricted Delaunay triangulation on curves, and is still a subset of it on surfaces, under mild sampling conditions. In this paper, we prove that these results do not extend to higher-dimensional manifolds, even under strong sampling conditions such as uniform point density. On the positive side, we show how the sets of witnesses and landmarks can be enriched, so that the nice relations that exist between restricted Delaunay triangulation and witness complex hold on higher-dimensional manifolds as well. We derive from our structural results an algorithm that reconstructs manifolds of any arbitrary dimension or co-dimension at different scales. The algorithm combines a farthest-point refinement scheme with a vertex pumping strategy. It is very simple conceptually, and it does not require the input point sample to be sparse. Its running time is bounded by c(d)n ², where n is the size of the input point cloud, and c(d) is a constant depending solely (yet exponentially) on the dimension d of the ambient space. Although this running time makes our reconstruction algorithm rather theoretical, recent work has shown that a variant of our approach can be made tractable in arbitrary dimensions, by building upon the results of this paper. This work was done while S.Y. Oudot was a post-doctoral fellow at Stanford University. His email there is no longer valid.     

An inequality for polyhedra and ideal triangulations of cusped hyperbolic 3-manifolds

It is not known whether every noncompact hyperbolic 3-manifold of finite volume admits a decomposition into ideal tetrahedra. We give a partial solution to this problem: Let be a hyperbolic 3-manifold obtained by identifying the faces of convex ideal polyhedra . If the faces of are glued to , then can be decomposed into ideal tetrahedra by subdividing the 's.

     

Distance-restricted matching extension in planar triangulations

A graph G is said to have property E(m,n) if it contains a perfect matching and for every pair of disjoint matchings M and N in G with |M|=m and |N|=n, there is a perfect matching F in G such that M⊆F and N∩F=0?. In a previous paper (Aldred and Plummer 2001) [2], an investigation of the property E(m,n) was begun for graphs embedded in the plane. In particular, although no planar graph is E(3,0), it was proved there that if the distance among the three edges is at least two, then they can always be extended to a perfect matching. In the present paper, we extend these results by considering the properties E(m,n) for planar triangulations when more general distance restrictions are imposed on the edges to be included and avoided in the extension.     

A generating theorem of simple even triangulations with a finitizable set of reductions

We shall determine exactly two $(P,Q)$-irreducible even triangulations of the projective plane. This result is a new generating theorem of even triangulations of the projective plane, that is, every even triangulation of the projective plane can be obtained from one of those two $(P,Q)$-irreducible even triangulations by a sequence of two expansions called a $P$-expansion and a $Q$-expansion, which were used in Batagelj (1984, 1989), Drapal and Lisonek (2010). Furthermore, we prove that for any closed surface $F^2$ there are finitely many $(P,Q)$-irreducible even triangulations of $F^2$.