matlab nm - Introduction to Numerical Analysis Using MATLAB...

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Introduction to Numerical Analysis Using MATLAB By Dr Rizwan Butt
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CHAPTER ONE Number Systems and Errors Introduction It simply provides an introduction of numerical analysis. Number Representation and Base of Numbers Here we consider methods for representing numbers on computers. 1. Normalized Floating-point Representation It describes how the numbers are stored in the computers.
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CHAPTER 1 NUMBER SYSTEMS AND ERRORS 1 . Human Error It causes when we use inaccurate measurement of data or inaccurate representation of mathematical constants. 2. Truncation Error It causes when we are forced to use mathematical techniques which give approximate, rather than exact answer. 3. Round-off Error This type of errors are associated with the limited number of digits numbers in the computers.
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CHAPTER 1 NUMBER SYSTEMS AND ERRORS Effect of Round-off Errors in Arithmetic Operation Here we analysing the different ways to understand the nature of rounding errors. 1. Rounding off Errors in Addition and Subtraction It describes how addition and subtraction of numbers are performed in a computer. 2. Rounding off Errors in Multiplication It describes how multiplication of numbers are performed in a computer.
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CHAPTER 1 NUMBER SYSTEMS AND ERRORS 3. Rounding off Errors in Division It describes how division of numbers are performed in a computer. 4. Rounding off Errors in Powers and roots It describes how the powers and roots of numbers are performed in a computer.
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CHAPTER TWO Solution of Nonlinear Equations Introduction Here we discuss the ways of representing the different types of nonlinear equation f(x) = 0 and how to find approximation of its real root . Simple Root’s Numerical Methods Here we discuss how to find the approximation of the simple root (non-repeating) of the nonlinear equation f(x) = 0.
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CHAPTER 2 SOLUTI ON OF NONLI NEAR EQUATI ONS 1. Method of Bisection This is simple and slow convergence method (but convergence is guaranteed) and is based on the Intermediate Value Theorem. Its strategy is to bisect the interval from one endpoint of the interval to the other endpoint and then retain the half interval whose end still bracket the root. 2. False Position Method This is slow convergence method and may be thought of as an attempt to improve the convergence characteristic of bisection method. Its also known as the method of linear interpolation.
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CHAPTER 2 SOLUTI ON OF NONLI NEAR EQUATI ONS 3. Fixed-Point Method This is very general method for finding the root of nonlinear equation and provides us with a theoretical framework within which the convergence properties of subsequent methods can be evaluated. The basic idea of this method is convert the equation f(x) = 0 into an equivalent form x = g(x). 4. Newtons Method
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This note was uploaded on 11/12/2010 for the course MATH 267 taught by Professor Chandrasekhar during the Spring '10 term at Anna University.

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matlab nm - Introduction to Numerical Analysis Using MATLAB...

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