Introduction to Numerical Analysis and Scientific Computing

Chapter 1

Computer Number Systems and Floating Point Arithmetic

1.1Introduction

1.2Conversion from Base 10 to Base 2

1.2.1Conversion of the Integral Part

1.2.2Conversion of the Fractional Part

1.3Conversion from Base 2 to Base 10

1.3.1Polynomial Evaluation

1.3.2Conversion of the Integral Part

1.3.3Conversion of the HYactional Part

1.4Normalized Floating Point Systems

1.4.1Introductory Concepts

1.4.2IEEE Floating Point Systems

1.4.3Denormalized Numbers in MATLAB

1.4.4Rounding Errors in Floating Point Representation

1.5Floating Point Operations

1.5.1Algebraic Properties in Floating Point Operations

1.5.2The Problem of Absorption

1.5.3The Problem of Cancellation or Loss of Precision

1.6Computing in a Floating Point System

1.6.1Cardinality and ...