After the problem of solving a linear system, the problem of computing the eigenvalues and the eigenvectors of a real or complex matrix is one of most important problems of numerical linear algebra. Several methods exist, among which we mention Jacobi, Givens–Householder, divide-and-conquer, QR...
Panju, M.: Iterative Methods for Computing Eigenvalues and Eigenvectors. In the Waterloo Mathematics Review, University of Waterloo, pp. 9–18Maysum Panju, Iterative Methods for Computing Eigenvalues and Eigenvectors, The Waterloo Mathematics Review 1 (2011), 9-18....
Computation of fuzzy eigenvalues and fuzzy eigenvectors of a fuzzy matrix is a challenging problem. Determining the maximal and minimal symmetric solution can help to find the eigenvalues. So, we try to compute these eigenvalues by determining the maximal and minimal symmetric solution of the fully ...
eigenvectorseigenvalues/ B0210 Algebra C1110 Algebra C4140 Linear algebra (numerical analysis)Many engineering and scientific applications require the computation of eigenvalues (and eigenvectors) of very large symmetric or Hermitian matrices. We describe a Lanczos procedure which allows us to compute ...
Quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors. Phys. Rev. Lett. 83, 5162 (1999). Article ADS MATH Google Scholar Shor, P. W. Fault-tolerant quantum computation in Proc. 37th Conference on Foundations of Computer Science (IEEE, 1996), pp. 56-...
(eigenvalues and eigenvectors) incubate precious topological information about the network at hand, including connectivity, partitioning, node distance and centrality. Real networks might be very large in number of nodes; luckily, most real networks are sparse, meaning that the number of edges (binary...
I really doubt I will ever see a problem where you need to compute the Jordan canonical form, I have seen some problems where you needed to do some stuff with eigenvalues and eigenvectors but usually, you use linear algebra for solving the problem, not in the coding part. Imagine using it...
Eigenvalues and Eigenvectors Solving eigenvalue and eigenvector problem: Ax = kx To solve Ax = kx, we use the two norm square of Ax - kx. If any k and x satisfies Ax = kx, then the absolute value Ax - kx satisfies the minimum value 0. Paper: https://www.sciencedirect.com/science...
This result shows that the direction of the sensor output eigenvectors can provide different surface texture information, and different surface information can produce completely different eigenvector directions. Fig. 5D gives the eigenvalue of our proposed TWRC system when it traversed eight different ...
learning rule (Oja-N) for computing real symmetrical matrix eigenvalues and eigenvectors, the initial vector must be on Rn unit hyper-sphere surface, otherwise, the network may produce limit-time overflow. In order to get over this defect, a new neural network (lyNN) algorithm is proposed. ...