Square Root Method
The square root method is an algorithm which solves the Matrix Equation
 | (1) |
, with 
a 
Symmetric Matrix and g a given Vector. Convert to a Triangular Matrix such that | (2) |
is the Matrix Transpose. Then |  |  | (3) |
 | |  | (4) |
so
 | (5) |
 | |  | |
 | |  | |
 | |  | |
 | |  | |
 | |  | (6) |
These give
 | |  | |
 | |  | |
 | |  | |
 | |  | |
 | |  | (7) |
giving
from A. Now solve for k in terms of the 
s and g, | |  | |
 | |  | |
 | |  | (8) |
which gives
 | |  | |
 | |  | |
 | |  | (9) |
Finally, find
from the s and k, | | | |
 | | | |
 | |  | (10) |
giving the desired solution,
 | |  | |
 | |  | |
 | |  | |
| (11) |
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.
- Cantor's Paradox
- Cantor Square Fractal
- Cantor's Theorem
- Cap
- Capacity
- Capacity Dimension
- Carathéodory Derivative
- Carathéodory's Fundamental Theorem
- Cardano's Formula
- Cardinality
- Cardinal Number
- Cardioid
- Cardioid Caustic
- Cardioid Evolute
- Cardioid Inverse Curve
- Cardioid Involute
- Cardioid Pedal Curve
- Cards
- Carleman's Inequality
- Carlson-Levin Constant
- Carlson's Theorem
- Carlyle Circle
- Carmichael Condition
- Carmichael Function
- Carmichael Number