lect_6 - Introduction to Numerical Analysis for Engineers...

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Introduction to Numerical Analysis for Engineers Systems of Linear Equations – Cramer’s Rule – Gaussian Elimination • Numerical implementation • Numerical stability – Partial Pivoting – Equilibration – Full Pivoting • Multiple right hand sides • Computation count • LU factorization • Error Analysis for Linear Systems – Condition Number • Special Matrices – Iterative Methods • Jacobi’s method • Gauss-Seidel iteration • Convergence Numerical Marine Hydrodynamics Lecture 6 2.29
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Systems of Linear Equations Gaussian Elimination Back-Substitution Reduction Reduction Step k Step n-1 Numerical Marine Hydrodynamics Lecture 6 2.29
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Systems of Linear Equations Gaussian Elimination Reduction Partial Pivoting by Columns Step k New Row k Pivotal Elements New Row i Required at each step! Numerical Marine Hydrodynamics Lecture 6 2.29
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Gaussian Elimination Multiple Right-hand Sides Reduction Step k Computation Count k p n-k n k Reduction Step k Operations Total Computation Count Reduction Back Substitution Reduction for each right-hand side inefficient.
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lect_6 - Introduction to Numerical Analysis for Engineers...

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