Objective: Solve linear systems.

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Presentation transcript:

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. 1/22/2003 18-525: Gaussian Elimination

18-525: Gaussian Elimination What is the Matrix? Now back substitute…. http://www.math.bcit.ca/examples/ary_7_2/backgd3e.html 1/22/2003 18-525: Gaussian Elimination

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 1/22/2003 18-525: Gaussian Elimination

18-525: Gaussian Elimination Design Variables Fractional representation Bit constraints: Magnitude and precision Matrix dimensions Pipelining Parallelism 5 adders, multipliers, dividers? Implementing division 1/22/2003 18-525: Gaussian Elimination

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 http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/Review_Exercises/systemex.html 1/22/2003 18-525: Gaussian Elimination

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

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