Home → Magazine Archive → January 1975 (Vol. 18, No. 1)
Table of Contents
ACM president's letter: relation of ACM activities to finances
Jean E. Sammet
Page 1
Professionalism in the computing field
The term professional means different things to different people; nevertheless, there are certain general technical and social standards normally associated with a professional. Further, the term is more generally applied to
…
Aaron Finerman
Pages 4-9
Positivity and norms
Following some lines of joint work with A.S. Householder, the character and use of algebraic methods in the theory of norms is demonstrated. New results concerning norms with values in an Archimedian vector lattice (not necessarily …
F. L. Bauer
Pages 9-13
The lemniscate constants
The lemniscate constants, and indeed some of the methods used for actually computing them, have played an enormous part in the development of mathematics. An account is given here of some of the methods used—most of the derivations …
John Todd
Pages 14-19
On the stability of Gauss-Jordan elimination with pivoting
The stability of the Gauss-Jordan algorithm with partial pivoting for the solution of general systems of linear equations is commonly regarded as suspect. It is shown that in many respects suspicions are unfounded, and in general …
G. Peters, J. H. Wilkinson
Pages 20-24
Two Hadamard numbers for matrices
A discussion is given of two functions of the entries of a square matrix, both related to Hadamard's determinant theorem, which have some merits as alternatives to norm-bound “condition numbers.” One (for linear systems) is known …
Garrett Birkhoff
Pages 25-29
Perturbations of eigenvalues of non-normal matrices
The problem considered is to give bounds for finite perturbations of simple and multiple eigenvalues &lgr;i of nonnormal matrices, where these bounds are in terms of the eigenvalues {&lgr;i}, the departure from normality &sgr;, and the Frobenius …
A. van der Sluis
Pages 30-36
Elementary divisors of tensor products
The elementary divisors of a tensor product of linear transformations have been known for 40 years. This paper provides a short, easily accessible proof of these results, and points out an interesting combinatorial consequence …
Marvin Marcus, Herbert Robinson
Pages 36-39
Pseudoinversus and conjugate gradients
This paper is devoted to the study of connections between pseudoinverses of matrices and conjugate gradients and conjugate direction routines.
Magnus R. Hestenes
Pages 40-43
The new math of computer programming
Structured programming has proved to be an important methodology for systematic program design and development. Structured programs are identified as compound function expressions in the algebra of functions. The algebraic properties …
Harlan D. Mills
Pages 43-48
Storage-efficient representation of decimal data
Usually n decimal digits are represented by 4n bits in computers. Actually, two BCD digits can be compressed optimally and reversibly into 7 bits, and three digits into 10 bits, by a very simple algorithm based on the fixed-length …
Tien Chi Chen, Irving T. Ho
Pages 49-52
Connections between accuracy and stability properties of linear multistep formulas
This paper is concerned with stability and accuracy of families of linear k-step formulas depending on parameters, with particular emphasis on the numerical solution of stiff ordinary differential equations. An upper bound, p …
Werner Liniger
Pages 53-56
Stably updating mean and standard deviation of data
By considering the (sample) mean of a set of data as a fit to this data by a constant function, a computational method is given based on a matrix formulation and Givens transformations. The (sample) mean and standard deviation …
Richard J. Hanson
Pages 57-58
ACM forum
Pages 63-65