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.
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.
Chessboard Cover,On a chessboard，only one Square is different, called specific.Use the Divide-and-Conquer methods to solve the Chessboard Cover Problem.
By building a nonlinear function relationship between an d the error signal，this paper presents a no—
vel variable step size LMS(Least Mean Square)adaptive filtering algorithm．
Yet another Java implementation for the addictive Minesweeper game. This game comes with a number of options unavailable in Windows s version, such as allowing more than one mines in a Square.
We address the problem of blind carrier frequency-offset (CFO) estimation in quadrature amplitude modulation,
phase-shift keying, and pulse amplitude modulation
communications systems.We study the performance of a standard
CFO estimate, which consists of first raising the received signal to
the Mth power, where M is an integer depending on the type and
size of the symbol constellation, and then applying the nonlinear
least Squares (NLLS) estimation approach. At low signal-to noise
ratio (SNR), the NLLS method fails to provide an accurate CFO
estimate because of the presence of outliers. In this letter, we derive
an approximate closed-form expression for the outlier probability.
This enables us to predict the mean-Square error (MSE) on CFO
estimation for all SNR values. For a given SNR, the new results
also give insight into the minimum number of samples required in
the CFO estimation procedure, in order to ensure that the MSE
on estimation is not significantly affected by the outliers.
Ink Blotting
One method for escaping from a maze is via ‘ink-blotting’. In this method your starting Square
is marked with the number ‘1’. All free, valid Squares north, south, east and west around the
number ‘1‘ are marked with a number ‘2’. In the next step, all free, valid Squares around the two
are marked with a ‘3’ and the process is repeated iteratively until :
The exit is found (a free Square other than the starting position is reached on the very edge
of the maze), or,
No more free Squares are available, and hence no exit is possible.
