Hp 48g Graphing Calculator Manual de usuario descargar pdf (Pagina 180)

100

101

Ill-Conditioned and Singular Matrices

A singular matrix is a square matrix that doesn’t have an inverse.

You normally get an error if you use [llx) to find the inverse of a

a singular coefficient matrix.

The most common cause of singular matrices are equations within a

s}fstem of linear equations that are linear combinations of one another.

That is, the coefficients of one equation can be computed exactly

from the coefficients of the other. Two equations thus related are

linearly dependent and the set of equations as a whole referred to as

dependent.

If a set of equations is independent, but small changes in their

coefficients would make them dependent, then the set of equations

(and their corresponding matrix A) are said to be ill-conditioned.

To determine if a matrix is ill-conditioned;

1. Enter the matrix onto the stack.

2. Compute its condition number: Press fMTH | MflTR NCiRM

CuND . If it is large, then it is ill-conditioned. If the condition

number is on the order of 10^^, the HP 48 may not be able to

distinguish it from a singular matrix.

To use ill-conditioned matrices in solving systems of linear equa

tions:

1. Set flag-22: Press MODES) 22 fV-) F'LflG :3F . This is

the Infinite Result Exception flag that will keep you from getting

an error using a singular matrix.

2. Solve the system of linear equations. The HP 48 perturbs the

singular matrix by an amount that’s usually small compared to the

rounding error. The calculated result corresponds to that for a

matrix close to the original, ill-conditioned matrix.

3. Determine the accuracy of the computed solution using the

condition number as you would for any ill-conditioned matrix (see

“Determining the Accuracy of a Matrix Solution” below.

4. Compute the residual to test your results.

5. Resolve the system of linear equations using LSQ.

14-16 Matrices and Linear Algebra

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Hp 48g Graphing Calculator Manual de usuario Pagina 180

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