This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: AMS 210: Applied Linear Algebra October 27, 2009 AMS 210 Topics Today Problem Set 5 Midterm 2 Computational Complexity of Solving Systems of Linear Equations Solving Tridiagonal Systems Sparse Matrix Fillin Stable Elimination and Roundoff Error Condition Number of a Matrix Condition Number Examples AMS 210 Problem Set 5 Grades and solutions available on Blackboard. Mean of 93, median of 96, and standard deviation of 8. AMS 210 Midterm 2 November 5 during class. Scientific calculators, plus TI83/84/86, allowed. TI89class calculators (TI89/92, the HP48/49/50s/etc) disallowed. Example problems on Blackboard by end of today. AMS 210 Computational Complexity of Solving Systems of Linear Equations Gaussian Elimination: ( n 1) 2 + ( n 2) 2 + ··· + (1) 2 ≈ n 3 3 multiplications. GaussJordan Pivoting: ( n i + 1) n multiplications to eliminate x i from other equations, so approximately n 3 2 multiplications. Theorem: A system of n equations in n unknowns requires approimately n 3 3 multiplications (and subtractions) to solve by Gaussian elimination and n 3 2 multiplications to solve by pivoting. Either method requires approximately n 3 multiplications to invert an nby n matrix. For solving Ax = b for multiple righthand sides, LU generally best: n 2 for each new righthandside. Jacobi iteration requires n 2 multiplications per iteration. Can be better or worse than LU depending on sparsity and convergence rate....
View
Full Document
 Fall '09
 ShuaiXue
 Linear Algebra, Matrices, condition number, tridiagonal systems

Click to edit the document details