001_IntroNumeths

Introduction to
Numerical Analysis

Engr. John R. Dela Cruz, MSc., AAE, 1PHN, AMIRSE

Numerical Analysis

The study of algorithms that use numerical
approximation for the problems of
mathematical analysis.

Numerical Methods

A complete and unambiguous set of
procedures for the solution of a problem,
together with computable error estimates.

Why use Numerical Methods?

To solve problems that cannot be solved
exactly.

1x u2
−

e 2 du

2π −∞

Why use Numerical Methods?

To solve problems that are intractable.

Sources of Errors

There are two sources of errors:
1. Truncation or Chopping – simple

removal of digits after particular
number of digits

e.g. = 0. … … × 10

by means of truncation to limiting y to k digits, we

just remove … to produce the new

form:

= 0. … × 10



Absolute and Relative Errors

Absolute Error

= −!
= − " #! $

Relative Error (expressed in percentage)

= −!

= − " #! $

Problem # 1

During the elementary and high school days,
the constant % is approximated as 3.14.
During college, the constant is approximated
as 3.1416.
(a) Determine the absolute approximate error

in reference to the new approximation.
(b) Comparing the new and previous

approximates, how many percent is the
relative error?