Introduction to Numerical Analysis and Scientific Computing

Nabil Nassif, Dolly Khuwayri Fayyad

• Publisher: Chapman and Hall/CRC
• Year: 2016
• ISBN:
  9781482208764
• Edition: 1
• Topic: Matematica
• Subtopic: Matematica generale

Designed for a one-semester course, Introduction to Numerical Analysis and Scientific Computing presents fundamental concepts of numerical mathematics and explains how to implement and program numerical methods. The classroom-tested text helps students understand floating point number representations, particularly those pertaining to IEEE simple an

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 Distribution of Floating Point Systems

1.6.2A MATLAB Simulation of a Floating Point System

1.6.3Tips for Floating Point Computation

1.7Exercises

1.8Computer Projects

1.1 Introduction

The main objective of this chapter is to introduce the students to modes of storage of users’ numbers in a computer memory and as well providing the readers with basic concepts of computer arithmetic, referred to also as Floating Point Arithmetic. Although the principles covered are general and can apply to any finite precision arithmetic system, we apply those principles only to Single and Double Precision IEEE (Institute of Electrical and Electronics Engineers) systems. For additional detailed references, we refer to [8], [14], [19] and [23].

In this view, we start by describing computer number representation in the binary system that uses 2 as the base. Since the usual decimal system uses base 10, we discuss therefore methods of conversion from one base to another. The octal and hexadecimal systems (respectively, base 8 and base 16 systems) are also introduced as they are often needed as intermediate stages b...