lect_7 - Introduction to Numerical Analysis for Engineers...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
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 7 2.29
Background image of page 1

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

View Full DocumentRight Arrow Icon
Linear Systems of Equations Tri-diagonal Systems Forced Vibration of a String Finite Difference y(x,t) x i f(x,t) 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 Numerical Marine Hydrodynamics Lecture 7 2.29
Background image of page 2
Linear Systems of Equations Tri-diagonal Systems General Tri-diagonal Systems LU Factorization Numerical Marine Hydrodynamics Lecture 7 2.29
Background image of page 3

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

View Full DocumentRight Arrow Icon
Linear Systems of Equations Tri-diagonal Systems LU Factorization Reduction Forward Substitution Back Substitution LU Factorization: 2*(n-1) operations Forward substitution: n-1 operations Back substitution: n-1 operations Total: 4(n-1) ~ O(n) operations Numerical Marine Hydrodynamics Lecture 7 2.29
Background image of page 4
Image of page 5
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 / 17

lect_7 - Introduction to Numerical Analysis for Engineers...

This preview shows document pages 1 - 5. Sign up to view the full document.

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