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PY3CO2 Part II Numerical Methods II

 

 

I Gauss elimination and LU decomposition
Introduction to the Gnu Scientific Library (GSL); GSL handling of vectors and matrices;
LU decomposition using GSL; Introduction to LAPACK; LU decomposition using DGETRF

II Vector spaces and linear equations
Systems of m equations in n unknowns; Rank of a matrix

III Linear dependence, bases and dimension

IV The four fundamental spaces of linear algebra
Column space, null space, row space and left null space;
The fundamental theorem of linear algebra; Existence of inverses

V Orthogonality
Orthogonal subspaces; Second fundamental theorem of linear algebra;
Matrices and subspaces

VI Inner products and projections onto lines
Transpose of a matrix; Orthogonal bases, matrices and Gram-Schmidt orthogonalisation

VII QR decomposition
Householder transformation; QR factorisation by Householder transformation

VIII Eigenvalues and eigenvectors
Reduction to Hessenberg form and QR factorisation;
Inverse power method for inverses; Singular value decomposition
Norm and condition number of a matrix

IX Special functions
G and incomplete G functions; Bessel functions; Legendre polynomials

Course texts:
Linear algebra and its applications , 3rd Edn. Strang (Harcourt, Brace, Jovanovich)
LAPACK User's Guide 3rd Edn. ( SIAM )
Computational Physics Landau and Paez (Wiley)

GSL document

LAPACK document

notes I

notes II

notes III

C source files

bessel

bessel_recursion

block

dgeqp3

dgesvd

dgetrf

dgetri

dsteqr

dsytrd

Householder

legendre

LU_decomp

matrix

QR_decomp

SVD_decomp

vector

vector_in

vector_out


 

 

School of Physics, Trinity College Dublin, Dublin 2, Ireland.
Tel:+353 1 8961675, Fax:+353 1 6711759, e-mail: physics@tcd.ie
Contact: chris.smith@tcd.ie
Last updated: Apr 30 2012.

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