Table of Contents

Example of Power Iteration

Author: Philip Nelson

Language: C++

Description

This demonstrates the power iteration method on the tri-diagonal matrix used to solve the Elliptic ODE.

Output

The largest Eigenvalue of the NxN matrix with increasing N. Observe that as the size of the matrix increases, the largest Eigenvalue asymptotically approaches the value 4.

Example

int main()
{
  std::cout << "A\n" << SecOrdFinDifMethEllipticMat<double, 5>() << std::endl << std::endl;
  std::cout << "5x5" << std::endl;
  std::cout << powerIteration(SecOrdFinDifMethEllipticMat<double, 5>(), 1000u) << std::endl << std::endl;
  std::cout << "10x10" << std::endl;
  std::cout << powerIteration(SecOrdFinDifMethEllipticMat<double, 10>(), 1000u) << std::endl << std::endl;
  std::cout << "100x100" << std::endl;
  std::cout << powerIteration(SecOrdFinDifMethEllipticMat<double, 100>(), 1000u) << std::endl << std::endl;
  std::cout << "1000x10000" << std::endl;
  std::cout << powerIteration(SecOrdFinDifMethEllipticMat<double, 1000>(), 1000u) << std::endl;
}

Result

A
| -2     1     0  |
|  1    -2     1  |
|  0     1    -2  |

5x5
3.73205

10x10
3.91899

100x100
3.99852

1000x10000
3.99893

Last Modification date: 27 February 2018