 # Communications of the ACM

#### 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  …

#### 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 …

#### 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 …

#### 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 …

#### 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 …

#### 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 …

#### 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 …

This paper is devoted to the study of connections between pseudoinverses of matrices and conjugate gradients and conjugate direction routines.

#### 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 …

#### 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 …

#### 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 …

#### 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 …

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