PLUS Factorization of
Matrices
PLUS
factorization was proposed as a new framework of matrix factorization, A=PLUS,
where matrices P, L and U are almost the same as in LU
factorization, permutation, unit lower and upper triangular matrices,
respectively, and S is a very special matrix, which is unit, lower and
triangular, but only with a small number of non-zeros. Different from LU
factorization, all the diagonal elements of U in PLUS factorization are
customizable, i.e., the elements can be assigned by users almost freely. With
PLUS factorization, the matrix A is easily factorized further into a
series of special matrices similar to S. The new computational mechanics
with PLUS factorization has a few very elegant and promising properties that
other factorizations do not have, such as in-place computation and simple
inversion. PLUS factorization also allows of transforming integers reversibly
and losslessly if the diagonal elements of U are all designated as 1,
-1, i, or - i.
The theory was
mainly published in the following two papers:
* Pengwei Hao, "Customizable
Triangular Factorizations of Matrices", Linear Algebra and Its
Applications, Vol. 382, pp. 135-154, May 2004.
* Pengwei Hao and
Qingyun Shi, "Matrix
Factorization for Reversible Integer Mapping", IEEE Transactions on
Signal Processing, Vol. 49, No. 10, pp. 2314-2324, Oct. 2001.
It has applications in lossless source coding, fast image registration and fast volumetric data rendering.
All our
publications are downloadable on http://www.dcs.qmul.ac.uk/~phao/Papers/.
Our programs in C (its EXE version) and MATLAB are also
available for research ONLY, and please cite the above papers in your
publications.
For any
commercial applications, a written permission MUST be obtained from the
authors.
email: phao@cis.pku.edu.cn, phao@dcs.qmul.ac.uk