Horror matrices: glossary
-
A
Horror Matrix
for a sparse direct method is either singular, extremely ill-conditioned
(a large condition number), or has a random sparse pattern (which
causes catastrophic fill-in).
- fill-in: nonzero entries in L or U that do not appear in A
- factorization: L*U=A, where L is lower triangular and U is upper triangular
(for example)
- direct method: one that takes a fixed amount of work, in contrast to
iterative methods.
- transpose: in the transpose, A(i,j) and A(j,i) are swapped.
- band matrix: one whose nonzero entries lie close to the diagonal
- diagonal: entries A(i,i) are on the diagonal of A
- cols: columns of the matrix
-
try: a MATLAB statement that attempts to execute a block of code.
If it fails, the
catch part of the statement is executed.
- memory paths outgave: direct methods fail if they run out of memory
- NETLIB
- fractal banded mats: these don't exist (as far as I know),
but then neither does the frumious Bandersnatch.
- direct slash
and
backslash
- elim tree: the elimination tree of a sparse matrix, often used in direct methods.
- while
- max
- cond:
condition number. Thus "maxome foe" becomes "max cond foe", a foe with a
large condition number.
- tril:
the lower triangular part of a matrix.
- triu:
the upper triangular part of a matrix.
- speye:
sparse identity.
- nan:
not-a-number.
- condest:
condition number estimation, which requires (naturaly) and factorization of the
matrix first.
- out-core: short for out-of-core. "Out-of-core" methods keep most of
the factors, and sometimes the matrix itself, on disk, not in main memory.
They are able to factorize huge matrices (and thus more horrible...).
"Working out-of-core" means to do the factorization while most
of the factors are out-of-core.
- n: typically used for the dimension of a matrix (number of rows and columns).
A direct method finds pivots from 1 to n.
- for:
a for-loop statement.
- end
the end of a for-loop or other statement.
- gzip
and tar: creates an compressed archive,
typically used to distribute software, when it's done.
So naturally it appears at the end of the poem, when the work is done.
- author = 'mad visit', etc. Run the code in
MATLAB and see what it does.
perm is a permutation vector, and author(perm) is a permutation of 'mad visit'.
See also the Jabberwocky poem itself,
by Lewis Carroll.
Just the poem