Distributed Symbolic Computations
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Developing Scientific Computing Software: Current Processes And
DEVELOPING: SGIENffl&Pifli|ii^Mp| CURRENT PROCESSES" WMWiiiiia DEVELOPING SCIENTIFIC COMPUTING SOFTWARE MASTER OF APPLIED SCIENCE(2008) McMaster University COMPUTING AND SOFTWARE Hamilton, Ontario TITLE: Developing Scientific Computing Software: Current Processes and Future Directions AUTHOR: Jin Tang, M.M. (Nanjing University) SUPERVISOR: Dr. Spencer Smith NUMBER OF PAGERS: xxii, 216 n Abstract Considerable emphasis in scientific computing (SC) software development has been placed on the software qualities of performance and correctness. How ever, other software qualities have received less attention, such as the qualities of usability, maintainability, testability and reusability. Presented in this work is a survey titled "Survey on Developing Scien tific Computing Software, which is apparently the first conducted to explore the current approaches to SC software development and to determine which qualities of SC software are in most need of improvement. From the survey. we found that systematic development process is frequently not adopted in the SC software community, since 58% of respondents mentioned that their entire development process potentially consists only of coding and debugging. Moreover, semi-formal and formal specification is rarely used when developing SC software, which is suggested by the fact that 70% of respondents indicate that they only use informal specification. In terms of the problems in SC software development, which are dis covered by analyzing the survey results, a solution is proposed to improve the quality of SC software by using SE methodologies, concretely, using a modified Parnas' Rational Design Process (PRDP) and the Unified Software Development Process (USDP). A comparison of the two candidate processes is provided to help SC software practitioners determine which of the two pro cesses fits their particular situation. -
The Guide to Available Mathematical Software Problem Classification System
The Guide to Available Mathematical Software Problem Classification System Ronald F. Boisvert, Sally E. Howe and David K. Kahaner November 1990 U.S. DEPARTMENT OF COMMERCE National Institute of Standards and Technology Gaithersburg, MD 20899 100 U56 //4475 1990 C.2 NATIONAL, INSrrnJTE OF STANDARDS & TECHNOLOGY / THE GUIDE TO AVAILABLE MATHEMATICAL SOFTWARE PROBLEM CLASSIFICATION SYSTEM Ronald F. Boisvert Sally E. Howe David K. Kahaner U.S. DEPARTMENT OF COMMERCE National InstHute of Standards and Technology Center for Computing and Applied Mathematics Gaithersburg, MO 20899 November 1990 U.S. DEPARTMENT OF COMMERCE Robert A. Mosbacher, Secretary NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY John W. Lyons, Director 2 Boisvert, Howe and Kahaner own manuals or on-line documentation system. In order to determine what software is avail- able to solve a particular problem, users must search through a very large, heterogeneous collection of information. This is a tedious and error-prone process. As a result, there has been much interest in the development of automated advisory systems to help users select software. Keyword search is a popular technique used for this purpose. In such a system keywords or phrases are assigned to each piece of software to succinctly define its purpose, and the set of aU such keywords axe entered into a database. Keyword-based selection systems query users for a set of keywords and then present a fist of software modules which contain them. A major difficulty with such systems is that users often have trouble in providing the appropriate keywords for a given mathematical or statistical problem. There is such a wealth of alternate mathematical and statistical terminology that it would be a rare occurrence for two separate knowledgeable persons to assign the same set of keywords to a given software module. -
Performance Analysis of Effective Symbolic Methods for Solving Band Matrix Slaes
Performance Analysis of Effective Symbolic Methods for Solving Band Matrix SLAEs Milena Veneva ∗1 and Alexander Ayriyan y1 1Joint Institute for Nuclear Research, Laboratory of Information Technologies, Joliot-Curie 6, 141980 Dubna, Moscow region, Russia Abstract This paper presents an experimental performance study of implementations of three symbolic algorithms for solving band matrix systems of linear algebraic equations with heptadiagonal, pen- tadiagonal, and tridiagonal coefficient matrices. The only assumption on the coefficient matrix in order for the algorithms to be stable is nonsingularity. These algorithms are implemented using the GiNaC library of C++ and the SymPy library of Python, considering five different data storing classes. Performance analysis of the implementations is done using the high-performance computing (HPC) platforms “HybriLIT” and “Avitohol”. The experimental setup and the results from the conducted computations on the individual computer systems are presented and discussed. An analysis of the three algorithms is performed. 1 Introduction Systems of linear algebraic equations (SLAEs) with heptadiagonal (HD), pentadiagonal (PD) and tridiagonal (TD) coefficient matrices may arise after many different scientific and engineering prob- lems, as well as problems of the computational linear algebra where finding the solution of a SLAE is considered to be one of the most important problems. On the other hand, special matrix’s char- acteristics like diagonal dominance, positive definiteness, etc. are not always feasible. The latter two points explain why there is a need of methods for solving of SLAEs which take into account the band structure of the matrices and do not have any other special requirements to them. One possible approach to this problem is the symbolic algorithms. -
A Comparison of Six Numerical Software Packages for Educational Use in the Chemical Engineering Curriculum
SESSION 2520 A COMPARISON OF SIX NUMERICAL SOFTWARE PACKAGES FOR EDUCATIONAL USE IN THE CHEMICAL ENGINEERING CURRICULUM Mordechai Shacham Department of Chemical Engineering Ben-Gurion University of the Negev P. O. Box 653 Beer Sheva 84105, Israel Tel: (972) 7-6461481 Fax: (972) 7-6472916 E-mail: [email protected] Michael B. Cutlip Department of Chemical Engineering University of Connecticut Box U-222 Storrs, CT 06269-3222 Tel: (860)486-0321 Fax: (860)486-2959 E-mail: [email protected] INTRODUCTION Until the early 1980’s, computer use in Chemical Engineering Education involved mainly FORTRAN and less frequently CSMP programming. A typical com- puter assignment in that era would require the student to carry out the following tasks: 1.) Derive the model equations for the problem at hand, 2.) Find an appropri- ate numerical method to solve the model (mostly NLE’s or ODE’s), 3.) Write and debug a FORTRAN program to solve the problem using the selected numerical algo- rithm, and 4.) Analyze the results for validity and precision. It was soon recognized that the second and third tasks of the solution were minor contributions to the learning of the subject material in most chemical engi- neering courses, but they were actually the most time consuming and frustrating parts of computer assignments. The computer indeed enabled the students to solve realistic problems, but the time spent on technical details which were of minor rele- vance to the subject matter was much too long. In order to solve this difficulty, there was a tendency to provide the students with computer programs that could solve one particular type of a problem. -
Software for Numerical Computation
Purdue University Purdue e-Pubs Department of Computer Science Technical Reports Department of Computer Science 1977 Software for Numerical Computation John R. Rice Purdue University, [email protected] Report Number: 77-214 Rice, John R., "Software for Numerical Computation" (1977). Department of Computer Science Technical Reports. Paper 154. https://docs.lib.purdue.edu/cstech/154 This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact [email protected] for additional information. SOFTWARE FOR NUMERICAL COMPUTATION John R. Rice Department of Computer Sciences Purdue University West Lafayette, IN 47907 CSD TR #214 January 1977 SOFTWARE FOR NUMERICAL COMPUTATION John R. Rice Mathematical Sciences Purdue University CSD-TR 214 January 12, 1977 Article to appear in the book: Research Directions in Software Technology. SOFTWARE FOR NUMERICAL COMPUTATION John R. Rice Mathematical Sciences Purdue University INTRODUCTION AND MOTIVATING PROBLEMS. The purpose of this article is to examine the research developments in software for numerical computation. Research and development of numerical methods is not intended to be discussed for two reasons. First, a reasonable survey of the research in numerical methods would require a book. The COSERS report [Rice et al, 1977] on Numerical Computation does such a survey in about 100 printed pages and even so the discussion of many important fields (never mind topics) is limited to a few paragraphs. Second, the present book is focused on software and thus it is natural to attempt to separate software research from numerical computation research. This, of course, is not easy as the two are intimately intertwined. -
RESOURCES in NUMERICAL ANALYSIS Kendall E
RESOURCES IN NUMERICAL ANALYSIS Kendall E. Atkinson University of Iowa Introduction I. General Numerical Analysis A. Introductory Sources B. Advanced Introductory Texts with Broad Coverage C. Books With a Sampling of Introductory Topics D. Major Journals and Serial Publications 1. General Surveys 2. Leading journals with a general coverage in numerical analysis. 3. Other journals with a general coverage in numerical analysis. E. Other Printed Resources F. Online Resources II. Numerical Linear Algebra, Nonlinear Algebra, and Optimization A. Numerical Linear Algebra 1. General references 2. Eigenvalue problems 3. Iterative methods 4. Applications on parallel and vector computers 5. Over-determined linear systems. B. Numerical Solution of Nonlinear Systems 1. Single equations 2. Multivariate problems C. Optimization III. Approximation Theory A. Approximation of Functions 1. General references 2. Algorithms and software 3. Special topics 4. Multivariate approximation theory 5. Wavelets B. Interpolation Theory 1. Multivariable interpolation 2. Spline functions C. Numerical Integration and Differentiation 1. General references 2. Multivariate numerical integration IV. Solving Differential and Integral Equations A. Ordinary Differential Equations B. Partial Differential Equations C. Integral Equations V. Miscellaneous Important References VI. History of Numerical Analysis INTRODUCTION Numerical analysis is the area of mathematics and computer science that creates, analyzes, and implements algorithms for solving numerically the problems of continuous mathematics. Such problems originate generally from real-world applications of algebra, geometry, and calculus, and they involve variables that vary continuously; these problems occur throughout the natural sciences, social sciences, engineering, medicine, and business. During the second half of the twentieth century and continuing up to the present day, digital computers have grown in power and availability. -
SNC: a Cloud Service Platform for Symbolic-Numeric Computation Using Just-In-Time Compilation
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TCC.2017.2656088, IEEE Transactions on Cloud Computing IEEE TRANSACTIONS ON CLOUD COMPUTING 1 SNC: A Cloud Service Platform for Symbolic-Numeric Computation using Just-In-Time Compilation Peng Zhang1, Member, IEEE, Yueming Liu1, and Meikang Qiu, Senior Member, IEEE and SQL. Other types of Cloud services include: Software as a Abstract— Cloud services have been widely employed in IT Service (SaaS) in which the software is licensed and hosted in industry and scientific research. By using Cloud services users can Clouds; and Database as a Service (DBaaS) in which managed move computing tasks and data away from local computers to database services are hosted in Clouds. While enjoying these remote datacenters. By accessing Internet-based services over lightweight and mobile devices, users deploy diversified Cloud great services, we must face the challenges raised up by these applications on powerful machines. The key drivers towards this unexploited opportunities within a Cloud environment. paradigm for the scientific computing field include the substantial Complex scientific computing applications are being widely computing capacity, on-demand provisioning and cross-platform interoperability. To fully harness the Cloud services for scientific studied within the emerging Cloud-based services environment computing, however, we need to design an application-specific [4-12]. Traditionally, the focus is given to the parallel scientific platform to help the users efficiently migrate their applications. In HPC (high performance computing) applications [6, 12, 13], this, we propose a Cloud service platform for symbolic-numeric where substantial effort has been given to the integration of computation– SNC. -
Analysis and Verification of Arithmetic Circuits Using Computer Algebra Approach
University of Massachusetts Amherst ScholarWorks@UMass Amherst Doctoral Dissertations Dissertations and Theses March 2020 ANALYSIS AND VERIFICATION OF ARITHMETIC CIRCUITS USING COMPUTER ALGEBRA APPROACH TIANKAI SU University of Massachusetts Amherst Follow this and additional works at: https://scholarworks.umass.edu/dissertations_2 Part of the VLSI and Circuits, Embedded and Hardware Systems Commons Recommended Citation SU, TIANKAI, "ANALYSIS AND VERIFICATION OF ARITHMETIC CIRCUITS USING COMPUTER ALGEBRA APPROACH" (2020). Doctoral Dissertations. 1868. https://doi.org/10.7275/15875490 https://scholarworks.umass.edu/dissertations_2/1868 This Open Access Dissertation is brought to you for free and open access by the Dissertations and Theses at ScholarWorks@UMass Amherst. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of ScholarWorks@UMass Amherst. For more information, please contact [email protected]. ANALYSIS AND VERIFICATION OF ARITHMETIC CIRCUITS USING COMPUTER ALGEBRA APPROACH A Dissertation Presented by TIANKAI SU Submitted to the Graduate School of the University of Massachusetts Amherst in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY February 2020 Electrical and Computer Engineering c Copyright by Tiankai Su 2020 All Rights Reserved ANALYSIS AND VERIFICATION OF ARITHMETIC CIRCUITS USING COMPUTER ALGEBRA APPROACH A Dissertation Presented by TIANKAI SU Approved as to style and content by: Maciej Ciesielski, Chair George S. Avrunin, Member Daniel Holcomb, Member Weibo Gong, Member Christopher V. Hollot, Department Head Electrical and Computer Engineering ABSTRACT ANALYSIS AND VERIFICATION OF ARITHMETIC CIRCUITS USING COMPUTER ALGEBRA APPROACH FEBRUARY 2020 TIANKAI SU B.Sc., NORTHEAST DIANLI UNIVERSITY Ph.D., UNIVERSITY OF MASSACHUSETTS AMHERST Directed by: Professor Maciej Ciesielski Despite a considerable progress in verification of random and control logic, ad- vances in formal verification of arithmetic designs have been lagging. -
The Misfortunes of a Trio of Mathematicians Using Computer Algebra Systems
The Misfortunes of a Trio of Mathematicians Using Computer Algebra Systems. Can We Trust in Them? Antonio J. Durán, Mario Pérez, and Juan L. Varona Introduction by a typical research mathematician, but let us Nowadays, mathematicians often use a computer explain it briefly. It is not necessary to completely algebra system as an aid in their mathematical understand the mathematics, just to realize that it research; they do the thinking and leave the tedious is typical mathematical research using computer calculations to the computer. Everybody “knows” algebra as a tool. that computers perform this work better than Our starting point is a discrete positive measure people. But, of course, we must trust in the results on the real line, µ n 0 Mnδan (where δa denotes = ≥ derived via these powerful computer algebra the Dirac delta at a, and an < an 1) having P + systems. First of all, let us clarify that this paper is a sequence of orthogonal polynomials Pn n 0 f g ≥ not, in any way, a comparison between different (where Pn has degree n and positive leading computer algebra systems, but a sample of the coefficient). Karlin and Szeg˝oconsidered in 1961 (see [4]) the l l Casorati determinants current state of the art of what mathematicians × can expect when they use this kind of software. Pn(ak)Pn(ak 1):::Pn(ak l 1) Although our example deals with a concrete system, + + − Pn 1(ak)Pn 1(ak 1):::Pn 1(ak l 1) 0 + + + + + − 1 we are sure that similar situations may occur with (1) det . -
Addition and Subtraction
A Addition and Subtraction SUMMARY (475– 221 BCE), when arithmetic operations were per- formed by manipulating rods on a flat surface that was Addition and subtraction can be thought of as a pro- partitioned by vertical and horizontal lines. The num- cess of accumulation. For example, if a flock of 3 sheep bers were represented by a positional base- 10 system. is joined with a flock of 4 sheep, the combined flock Some scholars believe that this system— after moving will have 7 sheep. Thus, 7 is the sum that results from westward through India and the Islamic Empire— the addition of the numbers 3 and 4. This can be writ- became the modern system of representing numbers. ten as 3 + 4 = 7 where the sign “+” is read “plus” and The Greeks in the fifth century BCE, in addition the sign “=” is read “equals.” Both 3 and 4 are called to using a complex ciphered system for representing addends. Addition is commutative; that is, the order numbers, used a system that is very similar to Roman of the addends is irrelevant to how the sum is formed. numerals. It is possible that the Greeks performed Subtraction finds the remainder after a quantity is arithmetic operations by manipulating small stones diminished by a certain amount. If from a flock con- on a large, flat surface partitioned by lines. A simi- taining 5 sheep, 3 sheep are removed, then 2 sheep lar stone tablet was found on the island of Salamis remain. In this example, 5 is the minuend, 3 is the in the 1800s and is believed to date from the fourth subtrahend, and 2 is the remainder or difference. -
Performance Analysis of Effective Symbolic Methods for Solving Band Matrix Slaes
EPJ Web of Conferences 214, 05004 (2019) https://doi.org/10.1051/epjconf/201921405004 CHEP 2018 Performance Analysis of Effective Symbolic Methods for Solving Band Matrix SLAEs 1, 1, Milena Veneva ∗ and Alexander Ayriyan ∗∗ 1Joint Institute for Nuclear Research, Laboratory of Information Technologies, Joliot-Curie 6, 141980 Dubna, Moscow region, Russia Abstract. This paper presents an experimental performance study of imple- mentations of three symbolic algorithms for solving band matrix systems of linear algebraic equations with heptadiagonal, pentadiagonal, and tridiagonal coefficient matrices. The only assumption on the coefficient matrix in order for the algorithms to be stable is nonsingularity. These algorithms are implemented using the GiNaC library of C++ and the SymPy library of Python, considering five different data storing classes. Performance analysis of the implementations is done using the high-performance computing (HPC) platforms “HybriLIT” and “Avitohol”. The experimental setup and the results from the conducted computations on the individual computer systems are presented and discussed. An analysis of the three algorithms is performed. 1 Introduction Systems of linear algebraic equations (SLAEs) with heptadiagonal (HD), pentadiagonal (PD) and tridiagonal (TD) coefficient matrices may arise after many different scientific and engi- neering problems, as well as problems of the computational linear algebra where finding the solution of a SLAE is considered to be one of the most important problems. On the other hand, special matrix’s characteristics like diagonal dominance, positive definiteness, etc. are not always feasible. The latter two points explain why there is a need of methods for solving of SLAEs which take into account the band structure of the matrices and do not have any other special requirements to them. -
Sage: Unifying Mathematical Software for Scientists, Engineers, and Mathematicians
Sage: Unifying Mathematical Software for Scientists, Engineers, and Mathematicians 1 Introduction The goal of this proposal is to further the development of Sage, which is comprehensive unified open source software for mathematical and scientific computing that builds on high-quality mainstream methodologies and tools. Sage [12] uses Python, one of the world's most popular general-purpose interpreted programming languages, to create a system that scales to modern interdisciplinary prob- lems. Sage is also Internet friendly, featuring a web-based interface (see http://www.sagenb.org) that can be used from any computer with a web browser (PC's, Macs, iPhones, Android cell phones, etc.), and has sophisticated interfaces to nearly all other mathematics software, includ- ing the commercial programs Mathematica, Maple, MATLAB and Magma. Sage is not tied to any particular commercial mathematics software platform, is open source, and is completely free. With sufficient new work, Sage has the potential to have a transformative impact on the compu- tational sciences, by helping to set a high standard for reproducible computational research and peer reviewed publication of code. Our vision is that Sage will have a broad impact by supporting cutting edge research in a wide range of areas of computational mathematics, ranging from applied numerical computation to the most abstract realms of number theory. Already, Sage combines several hundred thousand lines of new code with over 5 million lines of code from other projects. Thousands of researchers use Sage in their work to find new conjectures and results (see [13] for a list of over 75 publications that use Sage).