Patrick C. Fischer
ABSTRACT
The routine described below is a modification of the Carnegie Tech (IT) Compiler system for the IBM-650, which will provide automatic empirical analysis of propagated and round-off errors in computation. In the modified system, three kinds of variables are admissable: fixed-point integers called I-variables; floating-point numbers called C-variables, which are considered to be exact values; and 2-word variables called Y-variables, in which one word is a floating-point number which represents the value of the variable and the other word represents a bound upon the propagated and round-off error present in that value. Statements written in the IT language may refer to any or all of these classes of variables. During the execution phase of a program, computation proceeds in typical fashion, except that each time a Y-variable is operated upon by the program, its error term is modified so as to represent a valid bound upon propagated and round-off error in the variable.
Recommendations
Round-off error for retarded ordinary differential equations: A priori bounds and estimates
Consider the numerical solution of a retarded ordinary differential equation (RODE) by some standard algorithms. For a linear RODE, we estimate the accumulated round-off error as a linear combination of the preceding local round-off errors, and we bound ...
A Round-Off Error Model with Applications to Arithmetic Expressions
An arithmetic expression is evaluated in a form most suitable to a given computing structure. To select this “suitable form” restructuring algorithms using laws of associativity, commutativity, and distributivity have been proposed. This raises the ...
The error analysis and harmonic wave correction of inductosyn
CAR'10: Proceedings of the 2nd international Asia conference on Informatics in control, automation and robotics - Volume 2In this paper, the precision of the inductosyn had been improved through study error characteristics of inductosyn and use error harmonic wave correction method. First The long period error and short period error of the inductosyn have been studied. And ...
Comments