This overview presents a discussion on several topics of importance shared by the fields of computational mathematics and computational statistics. A brief history of the advancements to the fields of mathematics and statistics leading to the modern computational era is provided, along with a discussion of the intersection of topics which comprise the two subjects. The foundational aspects shared by both computational mathematics and computational statistics are explored with elementary discussions suitable to nonexperts and aspiring students of the computational sciences. Finally, a discussion of the role played by computational mathematics and computational statistics in a few selected application areas is explored. © 2014 Wiley Periodicals, Inc. How to cite this article: WIREs Comput Stat AN INTRODUCTION TO COMPUTATIONAL MATHEMATICS AND COMPUTATIONAL STATISTICSV arious fields that comprise the greater forum of computational science possess a certain core of methodologies necessary for producing numerically founded solutions. Since the advent of the first computers, the fields of computational mathematics and computational statistics have rapidly emerged as distinct disciplines making many important contributions to this area. While each subject possesses its own primary studies, computational mathematics and computational statistics share common ground owing to the close relationship of the underlying subjects. In this paper we will examine the areas and ways in which the disciplines of computational mathematics and computational statistics converge. The first step in this process will be to define what exactly computational * Correspondence to: aduffy@math.fsu.edu Citilabs, Tallahassee, FL, USA Conflict of interest: The author has declared no conflicts of interest for this article. mathematics and computational statistics are and how they relate to their more theoretical parent subjects.The subject of computational mathematics is primarily concerned with ways in which to efficiently compute numerical solutions to mathematical problems which may be difficult or impossible to solve otherwise. Computational mathematics can be viewed as the application of the theory of numerical analysis where algorithms must be developed to adhere to the theoretical solution properties of convergence and stability in a finite precision environment, and implemented in a manner which allows for feasible computation with limited computing resources. In computational mathematics, feasible computation may require the use of limited memory algorithms or parallel computation to reduce run times. In the modern many-core computing era parallelization is a vital aspect, and some introductory texts covering the tools of computational mathematics teach parallel computing alongside traditional material such as the text of Karniadakis and Kirby. 1 The practicing computational mathematician is typically well versed in high performance computing and parallel algorithms, as they are often in the business of producing high performance mathematic...
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