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Present-day problem of engineering hydrological computations on the generalization of hydrological information in Russia and the ways of its solution

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RUSSIAN METEOROLOGY AND HYDROLOGY 2011年第7期36卷 482-491页

作者： Rozhdestvenskii, A. V. Lobanova, A. G. VO State Hydrol Inst St Petersburg 199053 Russia

The substantiation is given of the need to develop the scientific works on the regular generalization of hydrological characteristics in the Russian Federation by means of the preparation of scientific and applied reference books and/or Territorial Construction Standards on the Determination of Basic Design Hydrological Characteristics on the territory of responsibility of the Territorial Administrations for Hydrometeorological and Environmental Monitoring (TAHEMs) of Roshydromet. The methodology, technical support, and the need in the regular recomputation of maximum design water discharges for operating hydraulic structures are considered. The ways of solution of the major current problem in the field of engineering hydrological computations on the territorial generalization of hydrometeorological information in all TAHEMs and in the State Hydrological Institute are outlined.

关键词： Geological engineering Hydrology computational mathematics

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Methods in computational Science

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丛书名： computational Science & Engineering

2021年

作者： Johan Hoffman

ISBN: (数字)9781611976724

ISBN: (纸本)9781611976717

computational methods are an integral part of most scientific disciplines and a rudimentary understanding of their potential and limitations is essential for any scientist or engineer. This textbook introduces computational science through a set of methods and algorithms with the aim of familiarizing the reader with the field's theoretical foundations and providing the practical skills to use and develop computational methods.

Methods in computational Science

extends the classical syllabus with new material, including high performance computing, adjoint methods, machine learning, randomized algorithms, and quantum computing;
is centered around a set of fundamental algorithms presented in the form of pseudocode;
presents theoretical material alongside several examples and exercises; and
provides Python implementations of many key algorithms.

关键词： computational science and engineering computational mathematics computer science data science scientific computing numerical analysis numerical linear algebra differential equation machine learning high performance computing optimization adjoint method

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On the cost of iterative computations

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PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES 2020年第2166期378卷 20190050-20190050页

作者： Carson, Erin Strakos, Zdenek Charles Univ Prague Fac Math & Phys Prague 18675 Czech Republic

With exascale-level computation on the horizon, the art of predicting the cost of computations has acquired a renewed focus. This task is especially challenging in the case of iterative methods, for which convergence behaviour often cannot be determined with certainty a priori (unless we are satisfied with potentially outrageous overestimates) and which typically suffer from performance bottlenecks at scale due to synchronization cost. Moreover, the amplification of rounding errors can substantially affect the practical performance, in particular for methods with short recurrences. In this article, we focus on what we consider to be key points which are crucial to understanding the cost of iteratively solving linear algebraic systems. This naturally leads us to questions on the place of numerical analysis in relation to mathematics, computer science and sciences, in general. This article is part of a discussion meeting issue 'Numerical algorithms for high-performance computational science'.

关键词： computational mathematics matrix computations high performance computing iterative methods

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Reproducibility and variable precision computing

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INTERNATIONAL JOURNAL OF HIGH PERFORMANCE COMPUTING APPLICATIONS 2020年第5期34卷 483-490页

作者： Bailey, David H. Lawrence Berkeley Natl Lab Berkeley CA 94720 USA Univ Calif Davis Dept Comp Sci Davis CA 95616 USA

Recently some scientific computing users have discovered that they can replace 64-bit with 32-bit operations for carefully selected portions of the computation, and still retain acceptable accuracy in the final results. In addition, developers of some emerging applications such as machine learning have discovered that they can achieve acceptable results with only 16-bit precision in certain portions of the code. At the other end of the precision spectrum, some users have explored using 128-bit arithmetic in some particularly demanding applications, while others have done computations using much higher precision-hundreds or even thousands of digits. Such work has underscored the need to develop new mathematical and software frameworks to support a dynamically variable level of precision, and, more generally, to rethink what "reproducibility" means in a variable precision environment. This article summarizes some of the work being done in this arena, and lists research problems that need to be solved.

关键词： Variable precision high precision reproducibility floating-point format computational mathematics

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DOMAIN CONTRACTIONS AROUND 3-DIMENSIONAL ANOMALIES IN SPHERICAL FINITE-DIFFERENCE COMPUTATIONS OF POISSON EQUATION: 收藏
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引用; SIAM JOURNAL ON APPLIED mathematics 1986年第6期46卷 1126-1149页; 作者： ZEMANIAN, AH ZEMANIAN, TS CORNELL UNIV DEPT CHEM ENGNITHACANY 14853; It is computationally advantageous to solve a finite-difference approximation to Poisson’s equation ∇⋅(σ∇P)<span class="mo" id="MathJax-Span-10" style="font-family: MathJax_Mai; It is computationally advantageous to solve a finite-difference approximation to Poisson’s equation $\nabla \cdot (σ \nabla P) + H = 0$; 来源：评论; 学校读者我要写书评

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Computer assisted solution of systems of two variable linear functional equations

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AEQUATIONES MATHEMATICAE 2020年第4期94卷 723-736页

作者： Borus, Gergo Gyula Gilanyi, Attila Univ Debrecen Inst Math Egyet Ter 1 H-4032 Debrecen Hungary Univ Debrecen Fac Informat Egyet Ter 1 H-4032 Debrecen Hungary

In the present paper, a general class of linear functional equations is considered and a computer program is described, which determines the exact solutions of systems of equations belonging to this class.

关键词： Linear functional equations Systems of functional equations Polynomials Monomials Computer assisted methods computational mathematics

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Using Jupyter for Reproducible Scientific Workflows

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COMPUTING IN SCIENCE & ENGINEERING 2021年第2期23卷 36-46页

作者： Beg, Marijan Taka, Juliette Kluyver, Thomas Konovalov, Alexander Ragan-Kelley, Min Thiery, Nicolas M. Fangohr, Hans Univ Southampton Fac Engn & Phys Sci Southampton SO17 1BJ Hants England Logilab F-75073 Paris France European XFEL D-22869 Schenefeld Germany Univ St Andrews Sch Comp Sci St Andrews KY16 9SX Fife Scotland Simula Res Lab Dept Sci Comp & Numer Anal N-1364 Fornebu Norway Univ Paris Saclay Lab Rech Informat CNRS F-91405 Orsay France Max Planck Inst Struct & Dynam Matter Computat Sci Grp D-22761 Hamburg Germany

Literate computing has emerged as an important tool for computational studies and open science, with growing folklore of best practices. In this work, we report two case studies-one in computational magnetism and another in computational mathematics-where domain-specific software was exposed to the Jupyter environment. This enables high level control of simulations and computation, interactive exploration of computational results, batch processing on HPC resources, and reproducible workflow documentation in Jupyter notebooks. In the first study, Ubermag drives existing computational micromagnetics software through a domain-specific language embedded in Python. In the second study, a dedicated Jupyter kernel interfaces with the GAP system for computational discrete algebra and its dedicated programming language. In light of these case studies, we discuss the benefits of this approach, including progress toward more reproducible and reusable research results and outputs, notably through the use of infrastructure such as JupyterHub and Binder.

关键词： Grid Computing mathematics Computing Micromagnetics Parallel Processing Python Scientific Information Systems Specification Languages Workflow Management Software Batch Processing HPC Resources Reproducible Workflow Documentation Jupyter Notebooks computational Micromagnetics Software Domain Specific Language Dedicated Jupyter Kernel Interfaces computational Discrete Algebra Dedicated Programming Language Reproducible Scientific Literate Computing Open Science Folklore computational Magnetism computational mathematics Jupyter Environment High Level Control Interactive Exploration Micromagnetics Mathematical Model Magnetic Domains Python computational Modeling Software Tools Analytical Models

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SINGULARLY PERTURBED BOUNDARY-VALUE PROBLEMS WITH ANGULAR LIMITING SOLUTIONS

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TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 1978年第JUL期241卷 155-182页

作者： HOWES, FA UNIV WISCONSIN DEPT MATHMADISONWI 53706

Abstract: A basic result of Haber and Levinson which describes the behavior of solutions of $\varepsilon y'' = f(t,y,y’)$,$a < t < b$,$y(a,\varepsilon )$,$y(b,\varepsilon )$, prescribed, in the presence of a reduced solution with corners is modified to treat related classes of problems. Under various stability assumptions, solutions are shown to remain, for small $\varepsilon > 0$, in a o(l)-neighborhood of an angular reduced solution with the possible exception of narrow layers near the boundaries in some cases. Each aspect of the theory developed here is illustrated by several examples.

关键词： Boundary value problems Boundary layers computational mathematics Mathematical constants College mathematics Toys Differential variability inequalities Definiteness

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Spatio-temporal efficiency measurement under undesirable outputs using multi-objective programming: a GAMS representation

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ANNALS OF OPERATIONS RESEARCH 2022年第2期311卷 1183-1202页

作者： Petridis, Konstantinos Univ Macedonia Dept Business Adm 156 Egnatia St Thessaloniki Greece

Time series data in DEA often represent successive versions of the same unit (DMU). In order to assess efficiency of each DMU, several DEA techniques have been employed. One of the problems that conventional DEA models face is that the reference set, when dealing with time series data, is not constructed correctly. This is attributed to the fact that conventional DEA models examine the DMUs and extract their efficiency scores based only the spatial dimension. However, when dealing with time series data for DMUs in the DEA context, the temporal dimension should be also taken into account. This paper is based on Spatio-Temporal DEA (ST-DEA) model (Petridis et al. in Ann Oper Res 238(1-2):475-496, 2016) and extends the presented S-T DEA model by incorporating undesirable inputs/outputs. A GAMS representation of the model for the solution and explanation of ST-DEA model is shown through an illustrative example. The scope of the paper is to analyze the concept of ST-DEA model and demonstrate its applicability via an application explained in GAMS optimization software.

关键词： Data envelopment analysis computational mathematics MOP Spatio-temporal efficiency GAMS

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The Extraordinary Power of Division in Straight Line Programs

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AMERICAN MATHEMATICAL MONTHLY 2012年第7期119卷 584-592页

作者： Borwein, Peter Hobart, Joe Simon Fraser Univ Dept Math Burnaby BC V5A 1S6 Canada Okanagan Coll Dept Math & Stat Kelowna BC V1Y 4X8 Canada

A lovely circle of ideas due primarily to Shub, Smale and Shamir says that if it is possible to divide quickly, then it is possible to factor quickly. Here, dividing quickly means modular division over a straight line program. In this context, quickly means actual computations done quickly. The point of this note is to advertise this lovely circle of ideas. The language of complexity theory sometimes clouds the underlying simplicity of the ideas. It is our hope to provide a straight forward explanation of these intrinsically simple ideas.

关键词： Algorithms Division Factorization computational mathematics Polynomials Mathematical constants Zero Binomial coefficients

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