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  • Verification methods: Rigor... Verification methods: Rigorous results using floating-point arithmetic
    Rump, Siegfried M. Acta numerica, 05/2010, Volume: 19
    Journal Article
    Peer reviewed

    A classical mathematical proof is constructed using pencil and paper. However, there are many ways in which computers may be used in a mathematical proof. But ‘proof by computer’, or even the use of ...
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  • Fast and accurate computati... Fast and accurate computation of the Euclidean norm of a vector
    Rump, Siegfried M. Japan journal of industrial and applied mathematics, 09/2023, Volume: 40, Issue: 3
    Journal Article
    Peer reviewed
    Open access

    The numerical computation of the Euclidean norm of a vector is perfectly well conditioned with favorite a priori error estimates. Recently there is interest in computing a faithfully rounded ...
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  • Cerebral amyloid-β PET with... Cerebral amyloid-β PET with florbetaben (18 F) in patients with Alzheimer's disease and healthy controls: a multicentre phase 2 diagnostic study
    Barthel, Henryk, Dr; Gertz, Hermann-Josef, MD; Dresel, Stefan, MD ... Lancet neurology, 05/2011, Volume: 10, Issue: 5
    Journal Article
    Peer reviewed

    Summary Background Imaging with amyloid-β PET can potentially aid the early and accurate diagnosis of Alzheimer's disease. Florbetaben (18 F) is a promising18 F-labelled amyloid-β-targeted PET tracer ...
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  • A note on Oishi’s lower bou... A note on Oishi’s lower bound for the smallest singular value of linearized Galerkin equations
    Rump, Siegfried M.; Oishi, Shin’ichi Japan journal of industrial and applied mathematics, 05/2024, Volume: 41, Issue: 2
    Journal Article
    Peer reviewed
    Open access

    Recently Oishi published a paper allowing lower bounds for the minimum singular value of coefficient matrices of linearized Galerkin equations, which in turn arise in the computation of periodic ...
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  • Mathematically rigorous glo... Mathematically rigorous global optimization in floating-point arithmetic
    Rump, Siegfried M. Optimization methods & software, 11/2018, Volume: 33, Issue: 4-6
    Journal Article
    Peer reviewed

    This paper gives details on how to obtain mathematically rigorous results for global unconstrained and equality constrained optimization problems, as well as for finding all roots of a nonlinear ...
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  • Learned Fitting of Spatiall... Learned Fitting of Spatially Varying BRDFs
    Merzbach, S.; Hermann, M.; Rump, M. ... Computer graphics forum, July 2019, 2019-07-00, 20190701, Volume: 38, Issue: 4
    Journal Article
    Peer reviewed

    The use of spatially varying reflectance models (SVBRDF) is the state of the art in physically based rendering and the ultimate goal is to acquire them from real world samples. Recently several ...
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  • Accurate Floating-Point Sum... Accurate Floating-Point Summation Part I: Faithful Rounding
    Rump, Siegfried M.; Ogita, Takeshi; Oishi, Shin'ichi SIAM journal on scientific computing, 01/2008, Volume: 31, Issue: 1
    Journal Article
    Peer reviewed

    Given a vector of floating-point numbers with exact sum $s$, we present an algorithm for calculating a faithful rounding of $s$, i.e., the result is one of the immediate floating-point neighbors of ...
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  • Faithfully Rounded Floating... Faithfully Rounded Floating-point Computations
    Lange, Marko; Rump, Siegfried M. ACM transactions on mathematical software, 09/2020, Volume: 46, Issue: 3
    Journal Article
    Peer reviewed

    We present a pair arithmetic for the four basic operations and square root. It can be regarded as a simplified, more-efficient double-double arithmetic. The central assumption on the underlying ...
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  • A branch-and-price approach... A branch-and-price approach for operational aircraft maintenance routing
    Sarac, Abdulkadir; Batta, Rajan; Rump, Christopher M. European journal of operational research, 12/2006, Volume: 175, Issue: 3
    Journal Article
    Peer reviewed

    In recent years, considerable effort in the field of operations research has been paid to optimizing airline operations, including the logistics of an airline’s fleet of aircraft. We focus on the ...
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