lect_3 - Introduction to Numerical Analysis for Engineers...

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Numerical Methods for Engineers 13.002 Lecture 3 Introduction to Numerical Analysis for Engineers • Systems of Linear Equations Mathews – Cramer’s Rule – Gaussian Elimination 3.3-3.5 • Numerical implementation 3.3-3.4 • Numerical stability – Partial Pivoting – Equilibration – Full Pivoting • Multiple right hand sides • Computation count • LU factorization 3.5 • Error Analysis for Linear Systems 3.4 – Condition Number • Special Matrices – Iterative Methods 3.6 • Jacobi’s method • Gauss-Seidel iteration • Convergence
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Numerical Methods for Engineers 13.002 Lecture 3 Systems of Linear Equations Cramer’s Rule Cramer’s Rule, n=2 Linear System of Equations Example, n=2 Cramer’s rule inconvenient for n>3
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Numerical Methods for Engineers 13.002 Lecture 3 Systems of Linear Equations Gaussian Elimination Reduction Step 0 Linear System of Equations
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Numerical Methods for Engineers 13.002 Lecture 3 Systems of Linear Equations Gaussian Elimination Reduction Step 1 i j
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lect_3 - Introduction to Numerical Analysis for Engineers...

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