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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Annals of operations research 24 (1990), S. 261-271 
    ISSN: 1572-9338
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract PL homotopy methods are effective numerical methods for highly nonlinear problems. It is widely believed that the feasibility of a PL homotopy method depends on the nondegeneracy condition that the zero set (or the fixed point set in the case of finding fixed points instead of zeroes) of the PL approximation of the homotopy does not intersect the triangulation's skeletons of co-dimensions two and above. This paper shows that, although the sections of the PL approximation's zero set tracked by the PL homotopy method are of dimension one (while other sections may have higher dimensions), the paths generated by the pivoting method are potentially and essentially of dimension two. It makes pathcrossing a safe thing. Thus, this paper first sets up the without exception feasibility of PL homotopy methods geometrically.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Acta mathematicae applicatae sinica 9 (1993), S. 135-142 
    ISSN: 1618-3932
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A PL homotopy algorithm is modified to yield a polynomial-time result on its computational complexity. We prove that the cost of locating all zeros of a polynomial of degreen to an accuracy of ε (measured by the number of evaluations of the polynomial) grows no faster thanO(max{n 4,n 3log2(n/ε)}). This work is in response to a question raised in a paper by S. Smale as to the efficiency of piecewise linear methods in solving equations. In comparison with a few results reported, the algorithm under discussion is the only one providing correct multiplicities and the only one employing vector labelling.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Acta mathematicae applicatae sinica 5 (1989), S. 310-317 
    ISSN: 1618-3932
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract PL homotopy methods are effective methods to locate zerces (or fixed points) of highly nonlinear mappings. Due to the lexicographical system, the methods are feasible without exceptions. This paper presents a geometrical interpretation of the without-exception feasibility.
    Type of Medium: Electronic Resource
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  • 4
    Publication Date: 2021-02-01
    Description: As data processing evolves towards large scale, distributed platforms, the network will necessarily play a substantial role in achieving efficiency and performance. Increasingly, switches, network cards, and protocols are becoming more flexible while programmability at all levels (aka, software defined networks) opens up many possibilities to tailor the network to data processing applications and to push processing down to the network elements. In this paper, we propose DPI, an interface providing a set of simple yet powerful abstractions flexible enough to exploit features of modern networks (e.g., RDMA or in-network processing) suitable for data processing. Mirroring the concept behind the Message Passing Interface (MPI) used extensively in high-performance computing, DPI is an interface definition rather than an implementation so as to be able to bridge different networking technologies and to evolve with them. In the paper we motivate and discuss key primitives of the interface and present a number of use cases that show the potential of DPI for data-intensive applications, such as analytic engines and distributed database systems.
    Language: English
    Type: conferenceobject , doc-type:conferenceObject
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