The class of iteration formulas obtainable by rational approximations of “Euler's formula” is derived with the corresponding error estimates. Some historical notes on iterative procedures are followed by a derivation of Euler's formula with the associated error estimate in a new notation which simplifies the error estimate and suggests generalizations. The final section considers the Padé approximants to the “Euler polynomial” and shows how a number of known formulas may be derived from this unified approach. There is a short discussion of the “best” formula.
In preparation for the widespread use of automatic scanners which will read documents and transmit their contents to other machines for analysis, this report presents a new concept in automatic analysis: the relative-frequency approach to measuring the significance of words, word groups, and sentences. The relative-frequency approach is discussed in detail, as is its application to problems of automatic indexing and automatic abstracting. Included in the report is a summary of automatic analysis studies published as of the date of writing. Conclusions are drawn that point toward more sophisticated mathematical and linguistic techniques for the solution of problems of automatic analysis.
Three iterative methods for calculation of nth roots (including one proposed by the author) are compared in two ways: (1) Theoretical convergence estimates are given. (2) A new macro-compiler which estimates machine running time is used to compare the running time of the three methods for a variety of input data.
The current University of North Carolina version of the IT Compiler [1, 2], as well as the GAT Compiler of Arden and Graham of the University of Michigan [3], have special “alphabetic read” and “alphabetic type” statements. On the UNIVAC 1105 these features allow the direct input or output of six-symbol words, each symbol being either an alphanumeric or special character. Internally, each symbol is represented by a six-bit binary coded decimal code. On the IBM 650, five-symbol words are processed, with each symbol represented internally by a two-digit decimal code.
The article by Lynn Yarbrough on Parallel Processing in the October Communications is interesting since it attracts attention to a subject which needs to be given increased consideration. His indictment of manufacturers for failing to provide what he feels is minimal to realizing the advantages of multi-programming is not applicable to STRETCH, however. It may be recalled that his specific complaint concerns the lack of protection of any program or monitor from the unpredictable actions of any other program. On page 15 of the STRETCH Data Processing System Reference Manual, we read: Address monitoring facilities are provided … The upper and lower boundaries of the storage area to be defined are placed in two address boundary registers. An alarm will be given when an address falls either inside or outside the defined area, whichever is desired. Storing in protected areas is normally suppressed.