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Chapter 2 System of Linear Equations Solving Linear Systems (2.4) January 26, 2010 New TA (2 TAs) Nejhum Shahed Office Hours: 2-5pm Wed, E309. Elementary Elimination Matrices. Example: Gaussian Elimination. Example: Gaussian Elimination. Example: Gaussian Elimination. LU Factorization. - PowerPoint PPT Presentation
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Chapter 2System of Linear Equations
• Solving Linear Systems (2.4)
January 26, 2010
New TA (2 TAs)Nejhum Shahed Office Hours: 2-5pm Wed, E309
Elementary Elimination Matrices
Example: Gaussian Elimination
Example: Gaussian Elimination
Example: Gaussian Elimination
LU Factorization
LU Factorization
Example: LU Factorization
Example: LU Factorization
What are M1, M1 A, M2 M2M1 A
A = LU, what are L and U ?
Row Interchanges
Partial Pivoting
LU Factorization with Partial Pivoting
Complete Pivoting
Example: Pivoting
Example: Small Pivots
Example, cont’d
Pivoting, cont’d
Residual
Residual
Example
Example
Uniqueness of LU Factorization
Complexity of Solving Linear Systems
Inversion vs. Factorization
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