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About the cover: THE COLORS OF COMPUTING

IP.com Disclosure Number: IPCOM000131302D
Original Publication Date: 1978-May-01
Included in the Prior Art Database: 2005-Nov-10
Document File: 2 page(s) / 19K

Publishing Venue

Software Patent Institute

Related People

True Seaborn: AUTHOR [+3]

Abstract

High-speed computing machines have led to a style of computing radically different from that in the old desk calculator days. Now one writes a program and submits it to a computer. In a batch environment, | results (answers or error messages) I are returned later and the validility of the answers depends on the care taken by the programmer. Even in an interactive environment the computation is done at such speed that only answers, in general, are returned to the user. If these are in the expected format and the values are not unreasonable, then users tend to assume they are correct.

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THIS DOCUMENT IS AN APPROXIMATE REPRESENTATION OF THE ORIGINAL.

This record contains textual material that is copyright ©; 1978 by the Institute of Electrical and Electronics Engineers, Inc. All rights reserved. Contact the IEEE Computer Society http://www.computer.org/ (714-821-8380) for copies of the complete work that was the source of this textual material and for all use beyond that as a record from the SPI Database.

About the cover: THE COLORS OF COMPUTING

High-speed computing machines have led to a style of computing radically different from that in the old desk calculator days. Now one writes a program and submits it to a computer. In a batch environment, | results (answers or error messages) I are returned later and the validility of the answers depends on the care taken by the programmer. Even in an interactive environment the computation is done at such speed that only answers, in general, are returned to the user. If these are in the expected format and the values are not unreasonable, then users tend to assume they are correct.

1

A project at the University of California at Santa Cruz plans to make more of the computational process visible. As a "planned" process this is a relatively new development, but the use of visual aids on-line in the computation process has been done in the pasty Successive approximations are displayed so the user can get a feeling for rates of convergence for a range of parameters. In some cases computational procedures coverage for awhile, then "blow up" as rounding errors, etc., take over control. For example, a Taylor approxe mation to a fifth- degree polynomial should be exact for six or more terms. Since differencing is notoriously sensitive to small errors, the numerical ) approximation will become worse as more and more terms are used.

The cover picture is a contour map of a function z=f~x,yJ, with the values - of z lying in specified intervals for t points displayed with the same color.

The system which does this kind of computation is based on a minicomputer (see Figure 1) with a student built vector arithmetic unit. Color pictures are developed in raster scan F form and displayed on a color moni for. The pictures with this article are photographs of that monitor.

Figure 2 shows a polynominal (in yellow) with the defining equation (F). The independent variable is shown in green. Figure 3 shows the approximate solutions (sine and cosine) for a pair of first order differential equations. Initial values range from O to 1 and from 1 to O with corresponding ; solution pairs in the same color.

The system is also designed to illustrate calculus and numerical analysis examples on-line. This means that programming must be minimized. Thus, a summation operator (++) approximates integration and z'-z produces the first difference of the function z. The red curve of Figure 4 is the "integral" of the polynomial, and the blue curve is the derivative displaced upward 5 units so that it may be easily...