Mathematical Subroutines Research Articles

Statistics on the use of mathematical subroutines from a computer center library

The Purdue University Computing Center has introduced a monitor into its operating system to gather statistics on the use of various system elements. A summary of these statistics for mathematical subroutines is presented here for a 3 month period (January 24, 1973, to April 20, 1973). Two tables are presented; Table 1 covers the use of the standard or built-in functions of high level languages (primarily Fortran). These functions have been grouped somewhat including putting complex and double-precision together with the ordinary versions of the functions. The maximum use of a complex and double-precision function occurs for ABS (2.2%) and EXPONENTIATION (1.5%), respectively. The total percentage of the use of complex and double-precision functions is 4.4% and 7.5% respectively. These values give estimates of the use of complex and double-precision arithmetic as follows:

Toward a definition of the term numerical mathematician

In attempting to evaluate the responses to the SIGNUM 1971 Nonacademic Numerical Mathematics Survey (see summary report published elsewhere in this Newsletter), it became clear that there is a need for a definition of the term "numerical mathematician". Without such a definition, the results of any such survey are necessarily ambigous. For example, our Laboratory employs over one hundred computer programmers, who frequently use mathematical subroutines in their codes. Are they numerical mathematicians? Furthermore, another hundred or more physicists and engineers are regular users of numerical methods. Should they be called numerical mathematicians?

The NASTRAN computer program for structural analysis

NASTRAN is a large digital computer program for static and dynamic structural analysis by the finite element approach. It is nearing completion after three years of development under NASA sponsorship. It will be made available to all interested users and it will be maintained by NASA. It is currently programmed for the IBM 360, the UNIVAC 1108, and the CDC 6600 computers. The major functional capabilities of NASTRAN are static analysis of structures with either linear or nonlinear material properties; buckling analysis; vibration modes analysis of either conservative or damped systems; frequency response analysis; and transient response analysis. Many convenience features are provided to the user including an extensive list of structural elements; the automatic generation of several types of loads including gravity loads and loads induced by thermal strains; plots of deformed and undeformed structures; and the choice of alternate methods of analysis, including, for example, either direct or modal formulations of dynamic problems. NASTRAN is intended primarily for large problems with hundreds or thousands of degrees of freedom. All mathematical subroutines have been designed to provide for the efficient solution of large problems by taking maximum advantage of matrix sparsity and bandedness. A flexible Executive System is provided that facilitates the addition of new functional capabilities to NASTRAN.

A Computer System for Signal Analysis at a Remote Terminal

A computer system which is operated from a remote terminal has been developed at Battelle Memorial Institute, Pacific Northwest Laboratories, to perform Fourier-transform analysis on time data rapidly and accurately. As many as 512 samples can be taken at frequencies up to 20 kHz, or digital data can be read directly into the computer memory. Fourier transforms, cross spectra, and autospectra can be determined for real or complex data. Hardware in the system consists of the computer and its standard peripherals; a general interface, which is a nonstandard peripheral device developed at Battelle-Northwest; and the communication link between the computer and the remotely located user. Software in the system is highly modular and consists of control and mathematical subroutines. Mathematical operations performed are the fast Fourier transform, complex multiplication, and conjugation. Transforms for 512 points can be calculated in five seconds, and a single real signal can be sampled and digitized at 20 kHz. Example calculations show that frequency components with relative amplitude ranges of five decades can be easily recognized. Calculation noise is a factor of a million less than the largest frequency component measured. The remote terminal allows the user with a complex experiment to have full-time direct access to the computer, but the computer room is not cluttered with his special-purpose experimental apparatus.