Chemical Engineering Hand Written_Notes_Part_46

Chemical Engineering Hand Written_Notes_Part_46 - 94 3....

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
94 3. LINEAR ALGEBRAIC EQUATIONS AND RELATED NUMERICAL SCHEMES gives an upper bound on the possible ampli f cation of errors in b while comput- ing the solution. 5.3.2. Case: Perturbation in matrix A. Suppose ,instead of solving for A x = b due to truncation errors we end up solving (5.41) ( A + δA )( x + δ x )= b Then by subtracting A x = b from the above equation we obtain (5.42) x + δA ( x + δ x )= 0 or (5.43) δ x = A 1 δA ( x + δ x ) Taking norm on both the sides, we have || δ x || = || A 1 δA ( x + δ x ) || (5.44) or || δ x || || A 1 || || δA || || x + δ x | (5.45) || δ x || / || x + δ x || ( || A 1 || || A || ) || δA || / || A || (5.46) || δ x || / || x + δ x || / || δA || / || A || C ( A )= || A 1 || || A || (5.47) Again,the condition number gives an upper bound on % change in solution to % error A. In simple terms, condition number of a matrix tells us how serious is the error in solution of A x = b due to the truncation or round o
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/26/2011 for the course EGN 3840 taught by Professor Mr.shaw during the Fall '11 term at FSU.

Page1 / 2

Chemical Engineering Hand Written_Notes_Part_46 - 94 3....

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online