Section 4: Using Matrix Operations; Understanding The Lu Decomposition - HP -15C Advanced Functions Handbook

Section 4
Using Matrix Operations
Matrix algebra is a powerful tool. It allows you to more easily
formulate and solve many complicated problems, simplifying
otherwise intricate computations. In this section you will find
information about how the HP-15C performs certain matrix
operations and about using matrix operations in your applications.
Several results from numerical linear algebra theory are
summarized in this section. This material is not meant to be self-
contained. You may want to consult a reference for more complete
presentations.*
Understanding the LU Decomposition
The HP-15C can solve systems of linear equations, invert matrices,
and calculate determinants. In performing these calculations, the
HP-15C transforms a square matrix into a computationally
convenient form called the L U decomposition of the matrix.
The L U decomposition procedure factors a square matrix A into
the matrix product LU. L is a lower-triangular matrixt with 1's on
its diagonal and with subdiagonal elements (those below the
diagonal) between —1 and +1, inclusive. U is an upper-triangular
matrix.! For example:
A =
2 3
1 1
1 0
.5 1
2 3
0 -.5
= LU.
* Two such references are
Atkinson, Kendall E., An Introduction to Numerical Analysis, Wiley, 1978.
Kahan, W. "Numerical Linear Algebra," Canadian Mathematical Bulletin, Volume 9,
1966, pp. 756-801.
f A lower-triangular matrix has O's for all elements above its diagonal. An upper-
triangular matrix has O's for all elements below its diagonal.
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