This web page contains example programs that will be covered in class.
Programs are written in Java and Matlab.
Web page in progress!!!
BASIC NUMERICAL ANALYSIS |
PROGRAM OUTPUT AND SOURCE CODE |
Loss of Numerical Precision.
This program illustrates the limitations of finite precision
representation of floating point numbers,
and how seemingly simple calculations can lead to a steady accumulation
of numerical errors.
This program works through three experiments:
(1) Simple arithmetic (4.0/3.0) with floating point (32-bit) numbers;
(2) Simple arithmetic (4.0/3.0) with double precision floating point (64-bit) numbers; and
(3) Simple arithmetic with a number (0.10) whose binary representation
contains an infinite series of digits.
|
Standalone Program:
NumericalPrecision.java Program Output: output |
Substractive Cancellation.
Subtractive cancellation occurs when two numbers of almost equal value are subtracted.
The result is a loss of significant digits.
This program illustrates two common strategies for avoiding
subtractive cancellation:
(1) rewrite arithmetic expressions to avoid subtraction; and
(2) replace an arithmetic expression with an approximation
that evaluates to a more accurate numerical value.
|
Standalone Program:
SubtractiveCancellation.java Program Output: output |
Root finding with the Method of Bisection.
Demonstrate use of bisection method to compute roots of the quadratic.
f(x) = (x-3)*(x-3) - 2; |
M-files:
myfunc3.m bisection.m testroot1.m Program Output: output |
Root finding with the Newton Raphson Algorithm.
Demonstrate use of newton-raphson algorithm by computing roots of
the quadratic equation
f(x) = (x-3)*(x-3) - 2; The derivative is given by: df(x)/dx = 2x - 6. |
M-files:
myfunc3.m myfunc3dfdx.m newtonraphson.m testroot2.m Program Output: output |
Gauss Elimination.
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M-files:
gaussnaive.m gausspivot.m testgauss1.m Program Output: output |
Gauss Seidel Iteration. |
M-files:
gaussseidel.m testgaussseidel.m Program Output: output |
ACKNOWLEDGEMENTS
Developed in February 2007 by Mark Austin
Copyright © 2007,
Department of Civil and Environmental Engineering, University of Maryland