## Microcomputer Algorithms: Action from AlgebraAlthough the computing facilities available to scientists are becoming more powerful, the problems they are addressing are increasingly complex. The mathematical methods for simplifying the computing procedures are therefore as important as ever. Microcomputer Algorithms: Action from Algebra stresses the mathematical basis behind the use of many algorithms of computational mathematics, providing detailed descriptions on how to generate algorithms for a large number of different uses. Covering a wide range of mathematical and physical applications, the book contains the theory of 25 algorithms. The mathematical theory for each algorithm is described in detail prior to discussing the algorithm in full, with complete program listings. The book presents the algorithms in modular form, allowing for easy interpretation, for the adaptation to readers' specific requirements without difficulty, and for use with various microcomputers. Blending mathematics and programming in one volume, this book will be of broad interest to all scientists and engineers, particularly those physicists using microcomputers for scientific problem handling. Students handling numerical data for research projects will also find the book useful. |

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### Contents

General Introduction | 1 |

Rootfinding Methods and their Application | 9 |

The Richardson Extrapolation Method | 25 |

Some Interpolation and Extrapolation Methods | 50 |

The Matrix Inverse and Generalized Inverse | 81 |

The Matrix Eigenvalue Problem | 99 |

Two Perturbation Methods | 142 |

Finite Difference Eigenvalue Calculations | 160 |

Recurrence Relation Methods | 187 |

Two Research Problems | 210 |

225 | |

231 | |

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### Common terms and phrases

9 REM algebra algorithm analysis and program angular momentum applied approximants array assignment statement BASIC BETOSC Boolean function coefficients column computed convergence derivative eigencolumn eigenvalue calculation energy levels error series error term estimate even-parity example expectation value factor FIDIF finite difference FOLDER folding formula GENFIT gives GO SUB h4 error HYPOSC integral interp interpolation inverse involves iterative Killingbeck leading error LET S=0 loop Mathematical theory matrix eigenvalue problem matrix elements matrix H microcomputer modified MOMOSC Newton's method obtained off-diagonal elements parameter parity perturbation theory perturbed oscillator polynomial potential power series PRINT E,F produce Program analysis program Lines Programming notes quantity quantum mechanical radial Rayleigh quotient recurrence relation Richardson extrapolation Romberg root root-finding approach root-finding module ROOTSCAN Schrodinger equation SECANT sequence SERAT SEROSC simple Sinclair basic singularity Specimen results stored strip subroutine Table transformation TWODOSC variable wavefunction WYNN ZEEMAN zero

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### References to this book

Computational Methods in Physics, Chemistry and Biology: An Introduction Paul Harrison Limited preview - 2001 |

Computational Methods in Physics, Chemistry and Biology: An Introduction Paul Harrison Limited preview - 2001 |