Lect_8_karimi - Introd uction to Num erical Analysis for Eng ineers System s o f Linear Eq uatio ns Cram er's Rule Gaussian Elim ination Num erical

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Lecture 7 Introduction to Num erical Analysis for Eng ineers System s of Linear Equations Cram er’s Rule Gaussian Elim ination • Num erical im plem entation • Num erical stability: Partial Pivoting , Equilibration, Full Pivoting • Multiple right hand sides • Com putation count • LU factorization Error Analysis for Linear System s Condition Num ber • Special Matrices Iterative Methods • Jacobi’s m ethod • Gauss-Seidel iteration • Convergence • Successive Overrelaxation Method • Gradient Methods 2.29 Numerical Marine Hydrodynamics Lecture 8
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Lecture 7 Linear System s of Equations Iterative Methods Sparse, Full-bandwidth Systems Rewrite Equations 0 x x 0 x 0 0 x 0 x 0 x x 0 0 x x 0 x Iterative, Recursive Methods 0 0 0 0 0 0 Gauss-Seidels’s Method Jacobi’s Method Numerical Marine Hydrodynamics Lecture 8 2.29
Background image of page 2
Linear System s of Equations Iterative Methods Convergence Jacobi’s Method Numerical Marine Hydrodynamics 2.29 Iteration – Matrix form Decompose Coefficient Matrix with / / Iteration Matrix form Convergence Analysis Sufficient Convergence Condition Note: NOT LU-factorization Lecture 8
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Lecture 7 Linear System s of Equations Iterative Methods Sufficient Convergence Condition Stop Criterion for Iteration Sufficient Convergence Condition Jacobi’s Method Diagonal Dominance + _ 2.29 Numerical Marine Hydrodynamics Lecture 8
Background image of page 4
Lecture 7 Linear System s of Equations Tri-diag onal System s Forced Vibration of a String Finite Difference Harmonic excitation f(x,t) = f(x) cos( ω t) Differential Equation Boundary Conditions Discrete Difference Equations Matrix Form Tridiagonal Matrix Symmetric, positive definite: No pivoting needed y(x,t) x i f(x,t) kh < 1 or kh > 3 y i ! 1 + (( kh ) 2 !
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/27/2012 for the course MECHANICAL 2.29 taught by Professor Henrikschmidt during the Spring '07 term at MIT.

Page1 / 20

Lect_8_karimi - Introd uction to Num erical Analysis for Eng ineers System s o f Linear Eq uatio ns Cram er's Rule Gaussian Elim ination Num erical

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online