Numerical Methods I - Basis and Fundamentals

An excellent textbook recommended by universities in several countries. Primarily written for students at technical universities, it is also very useful handbook for engineers, PhD students and scientists. The book introduces the reader into numeral systems, numbers in computers, types of variables and errors. Error analyses and error estimation are accomplished by various types of regression analyses that are usually used in an experimental work by engineers and scientists. It introduces the reader into numeral systems, numbers in computers, types of variables, types of errors and methods for finding roots of polynomials. Error analyses and error estimation are supplemented by various types of regression analyses that are usually used in an experimental work by engineers and scientists. Why are the presented topics so important? Simply, they are common to all numerical methods. Possibly, the most important parts are the descriptions of differences between constant (non-random) and random variables, related types of errors and error propaga�tions. Engineers and scientists sometimes ignore the difference between variables of different types, roughly interpreting all variables in their computations as constant variables. The consequence of such an approach is a wrong interpretation and estimation of the computation error. By understanding the sources and types of errors, they can be controlled and possibly reduced. That is of crucial importance in almost all sophisticated applications. The book is divided into seven chapters. In the first chapter, the historical back�ground and basic properties of various numeral systems, as well as conversion of numbers from one system to another are briefly explained. In the second chapter, numbers in digital computers, namely integers and floating point numbers are des�cribed. This helps the reader to choose precision and range limits of stored num�bers. The third chapter explains constant variables and related numerical errors, including error propagation and algorithm instability. The forth and fifth chapters explain random variables and related random errors, uncertainty, confi�dence level, as well as propagation of random errors. Various types of regression analyses of experimental data are described in the sixth chapter. Direct methods for finding roots of third and forth degree polynomials are described in the seventh chapter, followed by general iterative methods for polynomials of any degree. Practical application of the adopted knowledge is supported by 76 examples and 13 algorithms. In addition, the given text with 75 figures and 40 tables represents a valuable background for understanding, applying and developing various numerical analyses.