1. Objective: Solve linear systems.
Gaussian Elimination Algorithm Team W2
Matias Bombardi
Charles Kohl
Leon Mai
Jim Williams
Objective:
Implement algorithm to solve linear systems
Solve
Objective: Solve linear systems.
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18-525: Gaussian Elimination

2. 18-525: Gaussian Elimination
What is the Matrix?
Now back substitute….
1/22/2003
18-525: Gaussian Elimination

3. Estimate of Transistors
Component
How many
Transistor Count
Adder/Subtractor/Comparator 1
300
Multiplier
2800
Divider
3000
Control logic
2000
SRAM
160
960
Registers (w/ reset & set) 14
740
MUX 5
1250
Total:
11050
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18-525: Gaussian Elimination

4. 18-525: Gaussian Elimination
Design Variables
Fractional representation
Bit constraints: Magnitude and precision
Matrix dimensions
Pipelining
Parallelism
5 adders, multipliers, dividers?
Implementing division
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18-525: Gaussian Elimination

5. 18-525: Gaussian Elimination
Applications
Control systems
Traffic systems
Network flow
Robotics
Signal Processing
SPICE simulations
Solve large linear systems in pieces
Intersection near Present Location
40 + x + s = z
Intersection near Burger King
40 + t = y + s
Intersection near Apple Computer
60 + z = 50 + t
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18-525: Gaussian Elimination

6. 18-525: Gaussian Elimination
Design Alternatives
PS2 mod chip
-Too easy to implement/too small
Random number generator
Blowfish, CAST-256 encryption
-Needs too much SRAM to store tables (30k+ transistors)
Card game analyzer
-Issues with memory size and overall game AI quality
Cramer’s Rule
1/22/2003
18-525: Gaussian Elimination

7. 18-525: Gaussian Elimination
Questions?
1/22/2003
18-525: Gaussian Elimination