# lect_5 - Introduction to Numerical Analysis for Engineers...

This preview shows pages 1–4. Sign up to view the full content.

Numerical Methods for Engineers 13.002 Lecture 5 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

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

View Full Document
Numerical Methods for Engineers 13.002 Lecture 5 Linear Systems of Equations Tri-diagonal Systems y(x,t) x i Forced Vibration of a String f(x,t) Harmonic excitation f(x,t) = f(x) cos( Z t) Differential Equation Boundary Conditions Discrete Difference Equations Matrix Form Tridiagonal Matrix Finite Difference Symmetric, positive definite: No pivoting needed
Numerical Methods for Engineers 13.002 Lecture 5 Linear Systems of Equations Tri-diagonal Systems General Tri-diagonal Systems LU Factorization

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 10

lect_5 - Introduction to Numerical Analysis for Engineers...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online