Intro Numerical Analysis
Intro Numerical Analysis MATH 441
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This 2 page Class Notes was uploaded by Alphonso Thompson on Thursday October 29, 2015. The Class Notes belongs to MATH 441 at Western Carolina University taught by Erin McNelis in Fall. Since its upload, it has received 13 views. For similar materials see /class/230961/math-441-western-carolina-university in Mathematics (M) at Western Carolina University.
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Date Created: 10/29/15
MATH 441541 Numerical Analysis First Meeting Computer Number Representation and Arithmetic Thursday August 23 2007 Outline 1 Internal Number Representation a Bases Binary Decimal Hexidecimal Converting b Computer Floating Point Representation of Numbers IEEE Standard 7 BINARY y 71f 2cishift where s sign bit c 7 shift shifted exponent characteristic fractional part mantissa with double precision oating point numbers using 64 bit representation 1 bit for sign 3 11 bits for exponent c 52 bits for fraction 1 exponent c fraction 1 llllllllllllllllllllll i Determining the value of shift ii The number of numbers we can represent exactly iii The range of the numbers we can represent iv Plotting computer numbers to see the meshing pattern V Determining the pattern A Increasingdecreasing number of bits for c gt 7 B Increasingdecreasing number of bits for f gt 7 vi De nitions A Under ow B Over ow C Machine Epsilon e D Unit Roundoff u Normalized k Digit DEClMAL Floating Point Representation of Numbers A O V i0d1d2d3dk x10 d1 7amp0 d e 019 i Rounding vs Chopping ii Absolute and Relative Error 03 2 Computer Arithmetic a De nition of flz7 oating point representation of z flz z 1 67 where 6 lt u unit roundoff 10 Operations e 6 Stable Operations proving or disproving d Handout on Computations to Be Wary Of Rates of Convergence and Terminology a an a 04 with a rate of convergence Own