Work in progress, as of Sept 15, 2010

The Atanasoff-Berry-Computer (ABC) was a machine tailored to solving linear simultaneous equations with up to 29 unknowns and 50 bits of accuracy. It does this by forming one equation from two equations, with one variable of the two imput equations reduced to zero. Each of the input equations may have up to 29 variables.

In practice, there is a great deal of informed operator manipulation required:a) read keypunched decimal numbers into machine for conversion to equations in binary numbers b) machine punches out binary equations, one equation per intermediate card

with this conversion process completec) select and read two intermediate cards into the machine d) select which coefficient to reduce to zero e) start and monitor the machine (up to about 3 minutes) f) unload and label/store-in-bin the resulting punched intermediate card g) go back to c) above (about (unknowns-1)^2 times)

and when done processing the above,h) convert the intermediate binary results to decimal results for human use.

The construction and maintenance of the ABC machine and above operations seems impracticalfor the usual problems of 3 and 4 unknowns, common in many fields of activity.What "interesting" problems can be formulated in the required number of linear equations in say 8 to 29 unknowns?

Or phrasing the question another way,

Why 29 unknowns?

Atanasoff in his oral history mentions "complex spectra work".

Dr. George W. Snedecor may have been an actual user of the ABC machine results.Friends say "

circuit analysis"

Ronald Marks writes Sept 15, 2010 " This is a simple example of circuit analysis and its relationship to matrices. http://www.matrixlab-examples.com/linear-algebra-and-its-applications.html The attachment is an expanded version of the first example.

ABC-RonMarks-WritingMesh&NodalEquationsDirectlyMatrixForm.docLastly, is a 20 session Stanford video course - http://academicearth.org/courses/introduction-to-linear-dynamical-systems I will continue to look for more applicable stuff. Ron Marks"

Steven Winegarden notes that SPICE, a widely used electronics simulation program uses large simultaneous equations extensively to do its modeling. http://new.eetimes.com/design/automotive-design/4009934/Understand-basics-of-SPICE-environment-for-circuit-analysis-and-design-Part-1-of-2 contains the following: ABC-SPICE-Matrix.pdf. The following URLs (links) were found searching for "simultaneous" and "equations" that seemed to promise more than 6? unknowns.

Federal Reserve Bank of Atlanta

"A Simultaneous Equations Analysis of Analysts' Forecast Bias and Institutional Ownership"http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.34.4819&rep=rep1&type=pdf Bayesian Simultaneous Equations Analysis using Reduced Structures (1997)

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.30.716Simultaneous equations for circuit analysis : Worksheet

http://www.allaboutcircuits.com/worksheets/simultaneous.htmlSimultaneous Equations for Chemical Analysis

http://www.youtube.com/watch?v=7ntHNH3OMBkAnalysis of Soft Drinks" UV Spectrophotometry, Liquid Chromatography, and Capillary Electrophoresis

http://www.wfu.edu/chemistry/courses/jonesbt/280L/Experiment%207/softdrinks.pdfSimultaneous-Equations Bias and Agricultural Production Function Estimation

http://ageconsearch.umn.edu/bitstream/22659/1/08020161.pdfFrankly, I don't understand enough of the above to guess that these or other problems are sufficient to justify making the ABC machine in 1939 as a practical or commercial success - assuming the problem of creating and reading the intermediate equation storage cards had been made sufficiently reliable.

With great hind sight, one could suggest that a parity scheme of data validity checking would have been a good idea ;-)) Possibly 30 flip-flops with appropriate control circuitry could have validated the 30 data fields on each intermediate card - in forming the operator that there is likely a data error in this card.

This would immediately trigger "what to do now?" - but at least the operator knows there is a serious problem. This hind sight parity scheme could have been another invention for Atanasoff (or Berry) - this form of data validity checking was probably not invented/used until a few years later in magnetic tape technology - including IBM 7 track tapes.

If you have comments or suggestions, Send e-mail to Ed Thelen