Mercurial > hg > octave-nkf
changeset 18474:a4b4cf4c6ece stable
doc: update linear algebra chapter
author | Michael Godfrey <michaeldgodfrey@gmail.com> |
---|---|
date | Mon, 06 Jan 2014 20:36:44 -0500 |
parents | 5b88b2cb431e |
children | 61d9ef05b06b |
files | doc/interpreter/linalg.txi |
diffstat | 1 files changed, 25 insertions(+), 16 deletions(-) [+] |
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--- a/doc/interpreter/linalg.txi +++ b/doc/interpreter/linalg.txi @@ -20,10 +20,19 @@ @chapter Linear Algebra @cindex linear algebra -This chapter documents the linear algebra functions of Octave. -Reference material for many of these functions may be found in -Golub and Van Loan, @cite{Matrix Computations, 2nd Ed.}, Johns Hopkins, -1989, and in the @cite{@sc{lapack} Users' Guide}, SIAM, 1992. +This chapter documents the linear algebra functions provided in Octave. +Reference material for many of these functions may be found in Golub and +Van Loan, @cite{Matrix Computations, 2nd Ed.}, Johns Hopkins, 1989, and +in the @cite{@sc{lapack} Users' Guide}, SIAM, 1992. The +@cite{@sc{lapack} Users' Guide} is available at: +@cite{http://www.netlib.org/lapack/lug/} + +A common text for engineering courses is G. Strang, @cite{Linear Algebra +and Its Applications, 4th Edition}. It has become a widespread reference +for linear algebra. An alternative is P. Lax @cite{Linear Algebra and +Its Applications}, and also is a good choice. It claims to be suitable +for high school students with substantial mathematical interests as well +as first-year undergraduates. @menu * Techniques Used for Linear Algebra:: @@ -37,18 +46,18 @@ @section Techniques Used for Linear Algebra @cindex linear algebra, techniques -Octave includes a polymorphic solver, that selects an appropriate -matrix factorization depending on the properties of the matrix itself. -Generally, the cost of determining the matrix type is small relative to -the cost of factorizing the matrix itself, but in any case the matrix -type is cached once it is calculated, so that it is not re-determined -each time it is used in a linear equation. +Octave includes a polymorphic solver that selects an appropriate matrix +factorization depending on the properties of the matrix itself. +Generally, the cost of determining the matrix type is small relative to +the cost of factorizing the matrix itself. In any case the matrix type +is cached once it is calculated so that it is not re-determined each +time it is used in a linear equation. -The selection tree for how the linear equation is solve or a matrix -inverse is form is given by +The selection tree for how the linear equation is solved or a matrix +inverse is formed is given by: @enumerate 1 -@item If the matrix is upper or lower triangular sparse a forward or +@item If the matrix is upper or lower triangular sparse use a forward or backward substitution using the @sc{lapack} xTRTRS function, and goto 4. @c Permuted triangular matrices currently disabled in the code @@ -76,10 +85,10 @@ used with care. It should be noted that the test for whether a matrix is a candidate for -Cholesky@tie{}factorization, performed above and by the @code{matrix_type} -function, does not give a certainty that the matrix is +Cholesky@tie{}factorization, performed above, and by the @code{matrix_type} +function, does not make certain that the matrix is Hermitian. However, the attempt to factorize the matrix will quickly -flag a non-Hermitian matrix. +detect a non-Hermitian matrix. @node Basic Matrix Functions @section Basic Matrix Functions