Having great computational complexity and arithmeticcould be realizedinthe computerBythe numerical test toprovearithmeticis effictiveFor example, Getting the solution of a n order linearequations by Cramer ‘s Rule, we need do n!(n-1)(n+1)multiplicativecalculations.If n-20,we need do 9.7X1020 multiplicative calculations.With a ten million times floating-pointcomputer persecond to count,it need to use3oo thousand years.5)CommonlyusedmethodsDiscretization ; Recursion ; Replace Approximatively
⚫Having great computational complexity and arithmetic could be realized in the computer ⚫By the numerical test to prove arithmetic is effictive For example, Getting the solution of a n order linear equations by Cramer‘s Rule, we need do n!(n-1)(n+1) multiplicative calculations. If n=20，we need do 9.7×1020 multiplicative calculations. With a ten million times floating-point computer per second to count, it need to use 300 thousand years. 5) Commonly used methods Discretization ; Recursion ; Replace Approximatively
6)PracticalapplicationRealizing numerical calculation in computer based onMATLAB or other software , at the same time ,solvingthe practical problems
6) Practical application Realizing numerical calculation in computer based on MATLAB or other software , at the same time ,solving the practical problems
Question : What is calculationmthod is used to do ?MathematicalPracticalConstructionalgorithmmodelingproblemsProgramTo calculate the result in the computerdesign
• Question：What is calculation method is used to do ? Mathematical modeling Construction algorithm Program design To calculate the result in the computer Practical problems
s 2 Computer Machine Number System andFloating Point Arithmetic1. Binary digit system and computer machine digitsystem>In a computer-With thebinary representation ofreal numbers>In a computerConvert inputed decimal to binarynumber-Calculateinbinarynumber systemConvert result to decimal number
§2 Computer Machine Number System and Floating Point Arithmetic 1. Binary digit system and computer machine digit system ➢In a computer ➢In a computer ——With the binary representation of real numbers ——Convert inputed decimal to binary number ——Calculate in binary number system ——Convert result to decimal number
Example 1. Please x = 237 expresses as a binary numberSolutionFirst,xexpressed asx=237=1×27+1×26+1×25+0×24+1×23+1×22+0×2l+1×20Sothebinarynumber style ofxis:x = (11101101)
Solution First, x expressed as So the binary number style of x is: 7 6 5 4 3 2 1 0 x = = + + + + + + + 237 1 2 1 2 1 2 0 2 1 2 1 2 0 2 1 2 2 x = (11101101) Example 1. Please expresses as a binary number x = 237