A symmetric real matrix admits only real eigenvalues. We show how one can find these eigenvalues as well as their corresponding eigenvectors without using Mathematica's built-in commands (Eigenvalues and Eigenv
We first calculated the largest 50 eigenvalues by absolute value and the associated eigenvectors using the eigs function in MATLAB that is suited for sparse matrices and is based on the implicitly restarted Arnoldi iteration method28. We then selected the eigenvalues whose complex part was less than...
which also leads naturally to our proposed algorithm. In Sect.3we discuss the process of finding an appropriate type of the rational approximation. Section4is the main part where our eigenvalue-based algorithm is derived, and we prove its numerical stability in Sect.5. We present numerical expe...
The rest of this work is organized as follows. In Section2, we provide some basic theory on commuting families and eigenvalue condition numbers. In Section3we present our main algorithm (Algorithm 1) that uses a random linear combination to extract eigenvectors, followed by one- and two-sided...
Then instead of SVD you just find the eigenvectors of a 4×4 symmetric matrix, which is about 30% cheaper than SVD of 3×3 matrix. Also you don’t have to worry about handling special cases like reflections as in the SVD method. Check the Horn original paper: http://people.csail.mit...
in finding riccati solution of A*X+A'*X+X*W*X+Q that is X which stabilises A+W*X(real parts of eigen values are 0) This can be possible If...