Microcomputer Algorithms

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