Microcomputer Algorithms

John Killing beck has wrinen some eighty scientific publications, including five books. His publications range over the fields of group theory, perturbation theory and microcomputer numerical algorithms. He has been a visiting professor at the Universities of Guelph ( 197 4) and Besancon ( 1991). He was a Reader in Theoretical Physics at the University of Hull, where his plan to redeploy to computer science was halted by his enforced early retirement in 1989. He currently works part-time in the School of Mathematics at Hull, and intends to extend his freelance lecturing and writing activities.

Preface -- 1 General Introduction -- 1.1 The microcomputer style of programming -- 1.2 Modules and subroutines -- 1.3 Notation and conventions of this book -- 1.4 The program presentation format -- 1.5 Brief survey of chapter contents -- 2 Root-finding Methods and their Application -- 2.1 General introduction -- 2.2 The root-finding approach -- 2.3 Root-finding modules -- 2.4 A note on cubic equations -- 2.5 Brief program descriptions and programs ROOTSCAN. NEWTON. SECANT. ZIGZAG -- 2.6 Extrema and roots -- 2. 7 The programs SEARCH and MAXMIN -- 2.8 Expectation values. The integral approach -- 2.9 The energy approach -- 2.10 Calculating local quantities -- 3 The Richardson Extrapolation Method -- 3.1 General introduction -- 3.2-3.9 Microcomputer calculus. An example. Numerical differentiation. General applications. Richardson versus Pade. The residual error term. The standard extrapolation formulae. The non-standard case. The general case. The program RICH -- ROMBERG. Mathematical theory -- 3.10-3.14 Midpoint integration. Finding the AN , A modified midpoint rule. Relative merits of quadrature rules. Three-point rules -- ROMBERG. Programming notes -- 3.15-3.17 The subroutine structure. The two-point methods. Three-point rules -- 3.18 ROMBERG. Program analysis and program -- ROMBERG. Specimen results -- 3.19-3.22 The error integral. End-point singularities. Residual error examples. Final comments -- 4 Some Interpolation and Extrapolation Methods -- 4.1 General introduction -- INTERP. Mathematical theory -- 4.2-4.4 The Lagrange interpolation procedure. The divided difference approach. Computing derivatives. INTERP. Programming notes -- 4.5-4.7 Arrays. Variable indices. Derivatives -- 4.8 INTERP. Program analysis and program INTERP. Specimen results -- 4.9-4.10 Runge's example. Final comments. SPLINE and SPLEEN. Mathematical theory -- 4.11-4.13 Quadratic splines. The fundamental equations. The collocation method. SPLEEN -- 4.14 SPLINE. Program analysis and program SPLI