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This text explores aspects of matrix theory that are most useful in developing and appraising computational methods for solving systems of linear equations and for finding characteristic roots. Suitable for advanced undergraduates and graduate students, it assumes an understanding of the general principles of matrix algebra, including the Cayley-Hamilton theorem, characteristic roots and vectors, and linear dependence.
An introductory chapter covers the Lanczos algorithm, orthogonal polynomials, and determinantal identities. Succeeding chapters examine norms, bounds, and convergence;...

Automatic computing has undergone drastic changes since the pioneering days of the early Fifties, one of the most obvious being that today the majority of computer programs are no longer written in machine code but in some programming language like FORTRAN or ALGOL. However, as desirable as the time-saving achieved in this way may be, still a high proportion of the preparatory work must be attributed to activities such as error estimates, stability investigations and the like, and for these no programming aid whatsoever can be of help. In this respect, ALGOL, as an internationally...

Problem oriented programming languages as they have developed over the last ten years essentially serve two purposes which somewhat crudely can be described by the terms man-man communication and man-machine communication, respectively. As a carrier of information between humans, the problem oriented programming language is designed to express the essence of an algorithm in a way which is un ambiguous and concise as well as independent of (and therefore meaning ful without any reference to) the changing details of computing machine ry. As a carrier of information from man to computer, the...