# Numerical Analysis - Numerical Analysis Fall Semester...

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Chapter 12 / Exercise 47
Calculus
Stewart
Expert Verified
Numerical Analysis Fall Semester: LECTURER Professor Nir Sochen Office: 132 Location: Schreiber (Mathematics) E-mail: [email protected] Phone : 03-6408044 Meeting day: Sunday 10.00-12.00 INSTRUCTOR Ron Levie Office: Schreiber, room 11 E-mail: [email protected]
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Chapter 12 / Exercise 47
Calculus
Stewart
Expert Verified
Lecture 1: 12/10/2015 If we have a problem like: Ax=b, where A is a ? × ? matrix and x,b is an n dimensional vector then ? = ? −1 ? . Check notebook. This class will tackle cases where we have a problem (e.g. Ax=b) and it will give Algorithm(s) for the solution where: E=tolerance of the error From where we will have the Analysis of error. Floating Point representation: We would like to represent 9.75 in base 2: 9.75 = 8 + 1 + 1 2 + 1 4 = 2 3 + 2 0 + 2 −1 + 2 −2 = = 2 3 (2 0 + 2 −3 + 2 −4 + 2 −5 ) = ???????? × 2 ???????? = 1.00111 × 2 11 ± 0 0 1 1 1 0 0 1 1 This is an example Note: 11 ???? 2 = 3 ???? 10 Base 2: 0 0 1 1 10 2 11 3 100 4 Therefore ? = ±1. − − − − − − − − − × 2 −−−−−− = 64 ???? Problem (eg Ax=b) Algorithm(s) for solution E=tolerance of error Analysis of Error
Where ± is 1 bit 0/1 and the length after the 1. Is 52 bits and the power of 2 is 11 bits which is the way Matlab, C and C++ will represent in a double precision (e.g. double float). Therefore what is the range of possible numbers? What is the biggest number that can be represented? 0