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RMI &
Applications of Gauss Seidel
Method in the field of VLSI.
Arathi Manik Rathod(1MS22LVS02-T)

2. Gauss Seidel Method
• This method is a numeric iterative method to find an approximate solution of a
given system of linear equation.
• This is only applicable if the given system of linear equations is diagonally
dominant.
• Consider the following system of linear equations.
a11*x + a12*y + a13*z = b1
a21*x + a22*y + a23*z = b2
a31*x + a32*y + a33*z = b3
• Then we have by GSM:
x = 1/a11 [b1 – a12*y – a13*z]
y = 1/a22 [b2 – a21*x – a23*z]
z = 1/a33 [b3 – a31*x – a32*y]

3. Large Scale Circuit Simulation - Application
• Improvements in semiconductors have actually accelerated the
complexity of VLSI chips which potentially have hundreds of
thousands of transistors.
• To deal with this complexity two concepts are generally applied:
Decomposition – process of breaking a problem into manageable
pieces and Abstraction – which is the technique of hiding unnecessary
details.
• Applying these two principles in VLSI design results in a multi-level
hierarchical approach to the design of a complex chip.

4. The Hierarchy of Design Verification Tools

5. • For VLSI design, the major constraints are size, speed and power,
which are taken into consideration at each level.
• Therefore a number of simulations are required before the design is
completed.
• This research is concerned with the development of numerical
methods and scheduling techniques for fast and relatively accurate
time-domain simulation of MOS LSI and VLSI circuits.
• The basic approach in most large-scale circuit simulators is to first
partitioning of the circuit into smaller subcircuits, then to analyze
these subcircuits in a certain sequence.
• Traditionally, the Gauss-Seidel method has been used.

6. Point Gauss-Seidel Algorithm
• The linearized equation is of the form: A*x = B.
• We partition the matrix A into the form: A = L + D + U, where L, U, D
are lower triangular, upper triangular, and diagonal matrix.
• In Point Gauss-Seidel Algorithm, we use Gauss-Seidel method to solve
the equation.
• At every iteration, one solves a sequence of scalar equations of the
form :
gk (x1
n+1,x2
n+2,…….,xk-1
n+1,xk,xk+1
n,…,xm
n)=0

7. Point Gauss-Seidel Algorithm can be described as:

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