Introduction. 1. Computational Linear Algebra. Basic concepts and methods. Linear programming. LU decomposition. Inversion of symmetric, positive definite matrices. Tridiagonal systems of equations. Eigenvalues and eigenvectors of a symmetric matrix. Accuracy in algebraic computations. Ill-conditioned problems. Applications and further problems. 2. Nonlinear Equations and Extremum Problems. Nonlinear equations in one variable. Minimum of functions in one dimension. Systems of nonlinear equations. Minimization in multidimensions. Applications and further problems. 3. Parameter Estimation. Fitting a straight line by weighted linear regression. Mutivariable linear regression. Nonlinear least squares. Linearization, weighting and reparameterization. Ill-conditioned estimation problems. Multiresponse estimation. Equilibrating balance equations. Fitting error-in-variables models. Fitting orthogonal polynomials. Applications and further problems. 4. Signal Processing. Classical methods. Spline functions in signal processing. Fourier transform spectral methods. Applications and further problems. 5. Dynamical Models. Numerical solution of ordinary differential equations. Stiff differential equations. Sensitivity analysis. Quasi steady state approximation. Estimation of parameters in differential equations. Identification of linear systems. Determining the input of a linear system by numerical deconvolution. Applications and further problems. Subject Index.
This book gives a practical introduction to numerical methods and presents BASIC subroutines for real-life computations in the areas of chemistry, biology, and pharmacology. The choice of BASIC as the programming language is motivated by its simplicity, its availability on all personal computers and by its power in data acquisition. While most of the scientific packages currently available in BASIC date back to the period of limited memory and speed, the subroutines presented here can handle a broad range of realistic problems with the power and sophistication needed by professionals and with simple, step-by-step instructions for students and beginners.
Please note that a diskette containing the 37 program modules and 39 sample programs listed in the book is no longer available.
The main task considered in the book is that of extracting useful information from measurements via modelling, simulation, and statistical data evaluations. Efficient and robust numerical methods have been chosen to solve related problems in numerical algebra, nonlinear equations and optimization, parameter estimation, signal processing, and differential equations. For each class of routines an introduction to the relevant theory and techniques is given, so that the reader will recognise and use the appropriate method for solving his or her particular problem. Simple examples illustrate the use and applicability of each method.
- No. of pages:
- © Elsevier Science 1989
- 1st January 1989
- Elsevier Science
- eBook ISBN:
@qu:For many chemists who are concerned with mathematical and statistical aspects of their science this book will be a treasure trove, to be dipped into, sampled and used repeatedly. It is difficult to imagine a more practical aproach to the sorts of numerical problems that face the worker in various branches of physical chemistry. @source:Chromatographia
Eötvös Loránd University, Budapest, Hungary
Steven Vajda, Visiting Professor at Sussex University, formerly Professor of Operational Research, Department of Engineering Production, University of Birmingham.
Mount Sinai School of Medicine, New York, NY, USA