Exam 1: What will be covered

BRING A CALCULATOR !!!!

• Roundoff error:
  • One question about floating point arithmetic (given a arithmetic expression and a few numbers, evalutate it. E.g. Assume a floating point number system with three digits of accuracy. Evaluate: sqrt( (2.614)^2 - 4 ( 0.1524 ) ( 1.9331) )
  • One question about stability (e.g. like the question to show that adding n numbers gives a result like a_1 ( 1 + epsilon_1 ) + a_2 ( 1+epsilon_2 ) + a_3 ( 1+ ....)
• Using "blocked matrices": Something like given the following blocking of matrix L and vectors x and y, derive a column oriented algorithm for triangular solve.
• Solving linera systems
  • Derive an algorithm
  • derive cost of the algorithm
  • etc.
• compute the lu factorization, or triangular solve, or cholesky factorization or something like that for a given linear system.
• Polynomial interpolation: Compute the coefficients of a given system using XXX method. (Any method covered up to and including last thursday.

Old Exam