command \

[Christophe Prud'homme]

Hello

I am part of the team that writes "Scientific Computing with MATLAB" (*). We 
are now working on a new edition that will "work" with both matlab and octave 
with mentions of some differences or incompatibilities.
At some point we describe the command \ fpor Matlab, does it follow the same 
logic in octave or is it different ? here is what we have for matlab

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It is useful to know that the specific algorithm used by MATLAB when
the \ command is invoked depends upon the structure of the matrix A.
To determine the structure of A and select the appropriate algorithm,
MATLAB follows this precedence:

1. if A is sparse and banded, then banded solvers are used (like the
Thomas algorithm of Section 5.4). We say that a matrix A \220 Rm×n
(or in Cm×n) has lower band p if aij = 0 when i > j + p and upper
band q if aij = 0 when j > i + q. The maximum between p and q is
called the bandwidth of the matrix.

2. If A is an upper or lower triangular matrix (or else a permutation of
a triangular matrix), then the system is solved by a backsubstitution
algorithm for upper triangular matrices, or by a forward substitution
algorithm for lower triangular matrices. The check for triangularity
is done for full matrices by testing for zero elements and for sparse
matrices by accessing the sparse data structure.

3. If A is symmetric and has real positive diagonal elements (which does
not imply that A is positive definite), then a Cholesky factorization
is attempted (chol). If A is sparse, a preordering algorithm is applied
first.

4. If none of previous criteria are fulfilled, then a general triangular fac-
torization is computed by Gaussian elimination with partial pivoting
(lu).

5. If A is sparse, then the UMFPACK library is used to compute the
solution of the system.

6. If A is not square, proper methods based on the QR factorization
for undetermined systems are used (for the overdetermined case, see
Section 5.5).

(*)http://www.amazon.com/gp/product/3540443630/sr=8-3/qid=1141824041/ref=pd_bbs_3/104-1361323-2155125?%5Fencoding=UTF8
-- 
Christophe Prud'homme
Office MA B2 534
CMCS-IACS EPFL
CH-1015 Lausanne, Switzerland
Tel: +41 (0)21 693 25 47
Fax: +41 (0)21 693 43 03



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