The square root method is an algorithm which solves the Matrix Equation
|
(1) |
for , with
a Symmetric Matrix and g a given
Vector. Convert
to a Triangular Matrix such that
|
(2) |
where
is the Matrix Transpose. Then
so
|
(5) |
giving the equations
These give
giving
from A. Now solve for k in terms of the s and g,
which gives
Finally, find from the s and k,
giving the desired solution,
See also LU Decomposition
References
Kenney, J. F. and Keeping, E. S. Mathematics of Statistics, Pt. 2, 2nd ed. Princeton, NJ: Van Nostrand, pp. 298-300, 1951.
© 1996-9 Eric W. Weisstein
1999-05-26