{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

CSC_349_HANDOUT#6

# CSC_349_HANDOUT#6 - COMPUTER SCIENCE 349A Handout Number 6...

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

1 COMPUTER SCIENCE 349A Handout Number 6 CONDITION OF A PROBLEM Definition A problem whose (exact) solution can change greatly with small changes in the data defining the problem is called ill-conditioned . data { d i } exact solution { r i } defining a problem exact arithmetic perturbed problem, data { ˆ d i } = { d i + ε i } exact solution { ˆ r i } with ε i d i small exact arithmetic If there exist small i ε such that { ˆ r i } are not close to { r i }, then the problem is ill-conditioned . If { } { } i i r r ˆ for all small i ε , then the problem is well-conditioned . Example Consider the 3 × 3 system of linear equations b Hx = : = 60 / 47 12 / 13 6 / 11 5 / 1 4 / 1 3 / 1 4 / 1 3 / 1 2 / 1 3 / 1 2 / 1 1 3 2 1 x x x . Using the exact { } i d given above in the matrix H and the vector b , the exact solution is = 1 1 1 x .

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

CSC_349_HANDOUT#6 - COMPUTER SCIENCE 349A Handout Number 6...

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

View Full Document
Ask a homework question - tutors are online