Math 5610 - Computational Linear Algebra

---

Project maintained by BrandonFurman Hosted on GitHub Pages — Theme by mattgraham

The purpose of this page is to show how the condition number of the Hilbert matrix changes with size. This graph can be found belows.

From this graph it can be seen that the condition number for the Hilbert matrices grows exponentially. Past n = 10 the condition number became impossible to calculate with my functions due to the smallest eigenvalue approaching machine epsilon. The data for this graph was generated using the code below.

int maxIter = 10000;
double tol = 1e-12;

array2D A;

double condNum;

try {
	for (int m = 1; m < 11; m++) {
		A = HilbertMat(m);
		condNum = condNumApprox(A, tol, maxIter);
		std::cout << m << " " << condNum << std::endl;
	}
		
}
catch (const char* msg) {
	std::cout << msg << std::endl;
}