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A procedure for inverting large symmetric matrices
In the least squares method for simultaneous adjustment of several parameters, the coefficients of the normal equations are the elements of a symmetric positive-definite matrix. In order to solve the normal equations and evaluate the precision measures of the resulting parameters, inversion of this matrix of coefficients is required. Many available procedures for matrix inversion do not take advantage of the symmetry. Thus, when programmed for a high-speed computer, all n2 elements must be stored and manipulated, whereas only n(n + 1)/2 of them are independent. In order to allow a computer of given memory capacity to handle a large matrix, the following procedure for inverting a symmetric matrix has been devised.1
On translation of Boolean expressions
A program which translates an algorithmic language such as ALGOL into the machine language of an electronic computer performs the following functions:
Analysis. From the program in algorithmic language are determined the operations which the computer must perform in the execution of the target program and the logical interdependence of these.
Optimization. Of the many possibilities for optimization that exist, two are pertinent to this note: (2a) the elimination of superfluous operations, and (2b) the execution at translation time of those operations which do not depend on results produced by the target program.
Synthesis. The sequence of operations which arise from steps 1 and 2 is expressed in the language of the computer and placed into the target program.
Triangular walk pattern for the down-hill method of solving a transcendental equation
The down-hill method by Ward is a numerical method for determining a complex root of ƒ(z) = 0 and suitable for machine computation [1]. It is based on a theorem that W(z) = |Re(ƒ)| + |Im(ƒ)| (1) has minimum value, actually zero, at and only at a root of ƒ and seeks to minimize W by non-random walk from a starting point over the complex plane.
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