HP HP-15C Advanced Functions Handbook

110 Section 4: Using Matrix Operations
Note that rTE was scaled by 107 so that each row of E and A has
roughly the same norm as every other. Using this new system, the
HP-15C calculates the solution
2000.000080
1999.999980
1999.999980
1999.999980
1999.999980
, with AX =
107
-10"5
-9 X 10~6
0
0
This solution differs from the earlier solution and is correct to 10
digits.
Sometimes the elements of a nearly singular matrix E are
calculated using a formula to which roundoff contributes so much
error that the calculated inverse E"1 must be wrong even when it is
calculated using exact arithmetic. Preconditioning is valuable in
this case only if it is applied to the formula in such a way that the
modified row of A is calculated accurately. In other words, you
must change the formula exactly into a new and better formula by
the preconditioning process if you are to gain any benefit.
Least-Squares Calculations
Matrix operations are frequently used in least-squares calcula-
tions. The typical least-squares problem involves an n X p matrix
X of observed data and a vector y of n observations from which you
must find a vector b wiihp coefficients that minimizes
ill-
where r = y — Xb is the residual vector.
Normal Equations
From the expression above,
||r||| - (y - Xb)T(y - Xb) = yTy -
Solving the least-squares problem is equivalent to finding a
solution b to the normal equations

HP HP-15C Specifications

General

Brand	HP
Model	HP-15C
Category	Calculator
Language	English