BOOK REVIEWS FURTHER NUMERICAL METHODS IN BASIC, R. E. Scraton, 1986. No. of pages: 221.
The book consists of 14 chapters, plus a Preface, Index and a List of References.
In the Author's Preface, he justifies the use of BASIC for teaching numerical methods, stating that he prefers it to ALGOL, FORTRAN and PASCAL, because of BASIC's superior error trapping facilities. He further states that, because of this and because students have fewer problems with the syntax of the language, they learn more about numerical methods when using BASIC, a sentiment shared by the present reviewer.
Chapter 1 is on Matrix Iterative Methods, and commences by giving a review of eigenvalue theory. A theoretical treatment of convergence is discussed, together with the acceleration of convergence, where, in the case of the latter, an example is used with the aid of a microcomputer program.
Chapter 2 is on Matrix Eigenvalues, and commences by describing the use of the power method for determining dominant eigenvalues. The method is extended, where, through the use of deflation, the author shows how the other eigenvalues can be determined.
Chapter 3 is on Matrix Eigenvalues 11, where the author presents more powerful methods, such as that of Householder reduction, with the Sturm technique.
Chapter 4 is on Matrix Eigenvalues 111, where the author presents the LR and QR algorithms, and shows how to obtain complex eigenvalues with the aid of a microcomputer program.
Chapters 5 & 6 are on Boundary Value Problems, where the author presents the shooting method and the finite difference method.
Chapter 7 is on Hyperbolic Partial Differential Equations, where a numerical solution by the method of characteristics is presented, together with a computer implementation.
Chapter 8 is on Elliptic Partial Differential Equations, such as Laplace's equation and the Poisson