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Numerical Methods Cheat Sheet (DRAFT) by

This is a draft cheat sheet. It is a work in progress and is not finished yet.

Error

Forward Error
Backward Error
|r-x_a|
|f(r)-­f(x_a)|

Factor­ization

LU
PA=LU
Ax=b
Ax=b
A=LU
PAx=Pb and LUx=Pb
Lc=b
Lc=Pb
Ux=c
Ux=c
 

Elimin­ation Method­/Op­eration Count

Naive Guassian
(2/3)*n3
Back Substi­tution
k*n2
LU Factor­ization
(2/3)*n3
Twice Back Substi­tution
2k*n2

Error Magnif­ication Factor