chapter 2 system of linear equations solving linear systems (2.4) january 26, 2010 new ta (2 tas)
DESCRIPTION
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 PresentationTRANSCRIPT
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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
![Page 2: Chapter 2 System of Linear Equations Solving Linear Systems (2.4) January 26, 2010 New TA (2 TAs)](https://reader035.vdocuments.us/reader035/viewer/2022062322/56814743550346895db47ed5/html5/thumbnails/2.jpg)
Elementary Elimination Matrices
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Example: Gaussian Elimination
![Page 4: Chapter 2 System of Linear Equations Solving Linear Systems (2.4) January 26, 2010 New TA (2 TAs)](https://reader035.vdocuments.us/reader035/viewer/2022062322/56814743550346895db47ed5/html5/thumbnails/4.jpg)
Example: Gaussian Elimination
![Page 5: Chapter 2 System of Linear Equations Solving Linear Systems (2.4) January 26, 2010 New TA (2 TAs)](https://reader035.vdocuments.us/reader035/viewer/2022062322/56814743550346895db47ed5/html5/thumbnails/5.jpg)
Example: Gaussian Elimination
![Page 6: Chapter 2 System of Linear Equations Solving Linear Systems (2.4) January 26, 2010 New TA (2 TAs)](https://reader035.vdocuments.us/reader035/viewer/2022062322/56814743550346895db47ed5/html5/thumbnails/6.jpg)
LU Factorization
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LU Factorization
![Page 8: Chapter 2 System of Linear Equations Solving Linear Systems (2.4) January 26, 2010 New TA (2 TAs)](https://reader035.vdocuments.us/reader035/viewer/2022062322/56814743550346895db47ed5/html5/thumbnails/8.jpg)
Example: LU Factorization
![Page 9: Chapter 2 System of Linear Equations Solving Linear Systems (2.4) January 26, 2010 New TA (2 TAs)](https://reader035.vdocuments.us/reader035/viewer/2022062322/56814743550346895db47ed5/html5/thumbnails/9.jpg)
Example: LU Factorization
What are M1, M1 A, M2 M2M1 A
A = LU, what are L and U ?
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Row Interchanges
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Partial Pivoting
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LU Factorization with Partial Pivoting
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Complete Pivoting
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Example: Pivoting
![Page 15: Chapter 2 System of Linear Equations Solving Linear Systems (2.4) January 26, 2010 New TA (2 TAs)](https://reader035.vdocuments.us/reader035/viewer/2022062322/56814743550346895db47ed5/html5/thumbnails/15.jpg)
Example: Small Pivots
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Example, cont’d
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Pivoting, cont’d
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Residual
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Residual
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Example
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Example
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Uniqueness of LU Factorization
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Complexity of Solving Linear Systems
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Inversion vs. Factorization