# Lsq - HP 48gII Advanced User's Reference Manual

Graphing calculator.

...µ
Access:
Input/Output:
BESTFIT, COL , CORR, COV, EXPFIT, LINE, LINFIT, LOGFIT, PREDX, PREDY,
PWRFIT, XCOL, YCOL

## LSQ

Type:
Command
Description: Least Squares Solution Command: Returns the minimum norm least squares solution to any
system of linear equations where A × X = B.
If B is a vector, the resulting vector has a minimum Euclidean norm ||X|| over all vector
solutions that minimize the residual Euclidean norm ||A × X – B||. If B is a matrix, each
column of the resulting matrix, X
solutions that minimize the residual Euclidean norm ||A × X
If A has less than full row rank (the system of equations is underdetermined), an infinite number
of solutions exist. LSQ returns the solution with the minimum Euclidean length.
If A has less than full column rank (the system of equations is overdetermined), a solution that
satisfies all the equations may not exist. LSQ returns the solution with the minimum residuals of
A × X – B.
Access:
Flags:
Singular Values (-54)
Input/Output:
LQ, RANK, QR, /
LU
Type:
Command
Description: LU Decomposition of a Square Matrix Command: Returns the LU decomposition of a square
matrix.
When solving an exactly determined system of equations, inverting a square matrix, or
computing the determinant of a matrix, the hp49g+/hp48gII factors a square matrix into its
Crout LU decomposition using partial pivoting.
The Crout LU decomposition of A is a lower-triangular matrix L, an upper-triangular matrix U
with ones on its diagonal, and a permutation matrix P, such that P × A = L × U. The results
satisfy P × A L × U.
Model
Logarithmic
Exponential
Power
LR
Level 1/Argument 1
, has a minimum Euclidean norm ||X
i
L
OPERATIONS
LSQ
MATRIX LSQ
Level 2/Argument 1
Level 1/Argument 2
[ array ]
B
[[ matrix ]]
B
Transformation
y = b + m ln(x)
ln(y) = ln(b) + mx
ln(y) = ln(b) + m ln(x)
Level 2/Item 1
Intercept: x
( Ø is the left-shift of the 5key).
( ´ is the left-shift of the Pkey).
[[ matrix ]]
A
[[ matrix ]]
A
Full Command and Function Reference 3-99
Level 1/Item 2
Slope: x
1
|| over all vector
i
– B
||.
i
i
Level 1/Item 1
[ array ]
x
[[ matrix ]]
x
2  