Some Comments from a Numerical Analyst

@article{Wilkinson1971SomeCF,
  title={Some Comments from a Numerical Analyst},
  author={James Hardy Wilkinson},
  journal={J. ACM},
  year={1971},
  volume={18},
  pages={137-147}
}
A description is given of life with A. M. Turing at the National Physical Laboratory in the early days of the development of electronic computers (1946--1948). The present mood of pessimism among numerical analysts resulting from difficult relationships with computer scientists and mathematicians is discussed. It is suggested that in light of past and present performance this pessimism is unjustified and is the main enemy of progress in numerical mathematics. Some achievements in the fields of… 

Alan Turing and the origins of modern Gaussian elimination ∗

TLDR
The contributions of Alan Turing and other authors to the error analysis of Gaussian elimination, the historical context of these contributions, and their in uence on modern Numerical Analysis are revised.

The Legacy of Turing in Numerical Analysis

TLDR
It is argued that the contribution of Turing to "the other side of computer science", namely the domain of numerical computations as pioneered by Newton, Gauss, &c, and carried out today in the name of numerical analysis, is of an equally foundational nature.

Computer Science and its Relation to Mathematics

TLDR
A personal view of how this subject interacts with Mathematics is given, by discussing the similarities and differences between the two fields, and by examining some of the ways in which they help each other.

Alan Turing y los orígenes de la eliminación gaussiana moderna

TLDR
The purpose of this paper is to revise the contributions of Alan Turing and other authors to the error analysis of Gaussian elimination, the historical context of these contributions, and their influence on modern Numerical Analysis.

John von Neumann's Analysis of Gaussian Elimination and the Origins of Modern Numerical Analysis

TLDR
Just when modern computers were being invented, John von Neumann and Herman Goldstine wrote a paper to illustrate the mathematical analyses that they believed would be needed to use the new machines effectively and to guide the development of still faster computers.

Computer Science And Statistics

TLDR
This paper develops a theme about a specific, small part of the interface between computer science and statistics - that of kernels of computation - that is, the role of statisticians and numerical mathematicians in this field.

Alan turing and the other theory of computation

  • L. Blum
  • Computer Science
    ITiCSE '12
  • 2012
TLDR
This talk recognizes Turing's work in the foundations of numerical computation, and indicates its role in complexity theory today, and how it provides a unifying concept for the two major traditions in the Theory of Computation.

Software for roundoff analysis, II

TLDR
The package presented differs from Its predecessor in four important respects: a mmicompfler allows easy specicatmn of the algorithm being tested, the package can test the simultaneous effect of rounding error upon several values, and it deals with branching in numerical methods.

Recent Advances in the Computation of the Homology of Semialgebraic Sets

TLDR
This article describes recent advances in the computation of the homology groups of semialgebraic sets and throws light on the main features of this technical picture, the complexity results obtained, and how the new algorithms fit into the landscape of existing results.

A Personal Perspective on Numerical Analysis and Optimization

TLDR
A brief, non-technical, historical perspective on numerical analysis and optimization and how the area has developed over the past few decades and how it may continue is given.

References

SHOWING 1-8 OF 8 REFERENCES

Computational methods of linear algebra

The authors' survey paper is devoted to the present state of computational methods in linear algebra. Questions discussed are the means and methods of estimating the quality of numerical solution of

ROUNDING-OFF ERRORS IN MATRIX PROCESSES

A number of methods of solving sets of linear equations and inverting matrices are discussed. The theory of the rounding-off errors involved is investigated for some of the methods. In all cases

The bell laboratories numerical mathematics program library project

TLDR
Most computer facilities have “program libraries” that are inadequate, and when several routines are available which purport to do the same job, there is little or no indication as to which one is best, and under what circumstances.

Numerical inverting of matrices of high order

PREFACE 188 CHAPTER VIII. Probabilistic estimates for bounds of matrices 8.1 A result of Bargmann, Montgomery and von Neumann 188 8.2 An estimate for the length of a vector 191 8.3 The fundamental