lect_4 - Introduction to Numerical Analysis for Engineers...

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

View Full Document Right Arrow Icon
Numerical Methods for Engineers 13.002 Lecture 4 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
Background image of page 1

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

View Full DocumentRight Arrow Icon
Numerical Methods for Engineers 13.002 Lecture 4 Systems of Linear Equations Gaussian Elimination k p n-k Reduction Step k n k Computation Count Reduction Step k Operations Total Computation Count Reduction Back Substitution Multiple Right-hand Sides Reduction for each right-hand side inefficient. However, RHS may be result of iteration and unknown a priori (e.g. Euler’s method) -> LU Factorization
Background image of page 2
Numerical Methods for Engineers 13.002 Lecture 4 Systems of Linear Equations
Background image of page 3

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

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 09/13/2008 for the course CHE 348 taught by Professor Chelikowsky during the Spring '08 term at University of Texas at Austin.

Page1 / 12

lect_4 - Introduction to Numerical Analysis for Engineers...

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

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