25.12.2. Ill-Conditioned System

Try these first

1. 1.

   Define an ill-conditioned system.

   Hint

   Consider sensitivity to changes in data.

2. 2.

   What does a condition number of 1 indicate?

   Hint

   Think about stability and sensitivity.

3. 3.

   What happens in an ill-conditioned system?

   • Small changes have minor effects
   • Small changes lead to large errors
   • The system is always solvable

   Hint

   Consider how sensitivity impacts results.

4. 4.

   An ill-conditioned system typically has a condition number that is ____.

   • Close to 1
   • Greater than 1
   • Less than 1

   Hint

   Think about what condition numbers signify.

5. 5.

   A civil engineering project faces a potential ill-conditioned system with a high condition number. Discuss the implications for construction safety and suggest three corrective strategies to address potential issues.

   Hint

   Think about the roles of calculations and safety in construction.

6. 6.

   A system has a condition number of 1000. What does this imply? Provide an analysis of how this impacts solutions and engineering decisions.

   Hint

   Reflect on what sensitivity implies for real-world applications.