The module LSQ is for unconstrained linear least-squares fitting. It is
based upon Applied Statistics algorithm AS 274 (see comments at the start
of the module). A planar-rotation algorithm is used to update the QR-
factorization. This makes it suitable for updating regressions as more
data become available. The module contains a test for singularities which
is simpler and quicker than calculating the singular-value Decomposition.
An important feature of the algorithm is that it does not square the condition
number. The matrix X X is not formed. Hence it is suitable for ill-
conditioned problems, such as fitting polynomials.
By taking advantage of the MODULE facility, it has been possible to remove
many of the arguments to routines. Apart from the new function VARPRD,
and a back-substitution routine BKSUB2 which it calls, the routines behave
as in AS 274.
Included are the files wav1.m, wav2.m, wavecoef.mat and readme.
wav2 function implements the tree structured wavelet transform of the input matrix, up to the given level of Decomposition. Wav2 uses another function called wav1, which takes the well known wavelet transform of the given matrix. Daubechies wavelet coefficients are used for wavelet transform operation wahich is saved in wavcoeff.mat.
平均因子分解法，適用于正定矩陣First, let s recall the definition of the Cholesky Decomposition: Given a symmetric positive definite square matrix X, the Cholesky Decomposition of X is the factorization X=U U, where U is the square root matrix of X, and satisfies:
(1) U U = X
(2) U is upper triangular (that is, it has all zeros below the diagonal).
It seems that the assumption of positive definiteness is necessary. Actually, it is "positive definite" which guarantees the existence of such kind of Decomposition.
This collection of C++ templates wraps the FORTRAN or C interfaces for LAPACK so that they integrate with the Boost uBLAS library. Currently implements Cholesky Decomposition, LU Decomposition, inversion and determinant for general and positive-definite matrices.
Subroutine MCHOLSK :To solves a hermitian positive definite set of
complex linear simultaneous equations (AX=B) using the Cholesky
Decomposition method.
This demonstration shows that reordering the rows and columns of a sparse matrix S can affect the time and storage required for a matrix operation such as factoring S into its Cholesky Decomposition
The
Capacity of a MIMO channel with nt transmit antenna and nr recieve
antenna is analyzed. The power in parallel channel (after
Decomposition) is distributed as water-filling algorithm
