Research and Advances

A method for obtaining test matrices with a prescribed distribution of characteristic roots is given. The process consists of using particularly simple similarity transformations to generate full matrices from canonical forms. The matrices generated also have known characteristic vectors, inverses and determinants.

A general-purpose input routine is discussed and advocated for FORTRAN. The philosophy of such programs is examined and exemplified.

Solution of nonlinear two-point boundary-value problems is often an extremely difficult task. Quite apart from questions of reality and uniqueness, there is no established numerical technique for this problem. At present, shooting techniques are the easiest method of attacking these problems. When these fail, the more difficult method of finite differences can often be used to obtain a solution. This paper gives examples and discusses the finite difference method for nonlinear two-point boundary-value problems.

A set of subroutines for use in FORTRAN are described whose purpose is to synthesize output strings from (i) input strings which have been analysed by the SHADOW general syntactic analysis subroutine reported earlier, and/or (ii) packed BCD strings formed in any way. Function-type subroutines are included for intermediate manipulations, which are performed on the strings which are stored in an abbreviated internal representation. The automatic way in which an internal representation for each newly created substring is stored sequentially in a block of common storage, and the manner in which a storage block is dynamically allocated for that purpose, are discussed.

Use of linear programming models has grown so extensively in recent years that the whole concept for organizing a computer code has undergone a radical change. It no longer is adequate merely to reduce a mathematical algorithm (i.e. the simplex method) to a computer code. An advanced code must cope with such a variety of situations that the respective computer subprograms must be organized into an integrated system.Emphasis in this paper is devoted to the underlying principles upon which future linear programming systems must be based. These viewpoints are influenced by the new demands that applications within the petroleum industry are placing on such systems. Some of the components of such a system are: translation of problem statement in terms of basic data to linear programming matrix coefficients, data transmission for direct computer entry, data file at the computer center, data processing and editing prior to solving the simplex algorithm, an efficient and reliable code for solving the above-mentioned algorithm, and flexible means for summarizing the results.