In classical linear algebra, the eigenvalues of a matrix are sometimes defined as the roots of the characteristic polynomial. An algorithm to compute the roots of a polynomial by computing the eigenvalues of the corresponding companion matrix turns the tables on the usual definition. We derive a ...
Matrix algebraProblem solvingVector spacesIterative methodsTransformations(Mathematics)Numerical methods and proceduresTheoremsThe report describes the Givens-Householder method for finding the eigenvalues and eigenvectors of a real symmetric matrix. An attempt has been made to describe the method with detail ...
The kth transformation uses Householder reflections to introduce 20 Chapter 10. Eigenvalues and Singular Values zeros below the subdiagonal in the kth column. The result of this first phase is known as a Hessenberg matrix; all the elements below the first subdiagonal are zero. for k = 1:n-...
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...
Continued fraction calculation of the eigenvalues of tridiagonal matrices arising from the Schrodinger equation - Gerck, d’Oliveira () Citation Context ...nation) to change a given matrix to a upper Hessenberg matrix [1, 4, 11], and then to a similarly tridiagonal matrix, since there are ...
The kth transformation uses Householder reflections to introduce 20 Chapter 10. Eigenvalues and Singular Values zeros below the subdiagonal in the kth column. The result of this first phase is known as a Hessenberg matrix; all the elements below the first subdiagonal are zero. for k = 1:n-...
matrix algebraparallel processing/ sequential-parallel calculationeigenvaluessymmetric matricesalternating sequential-parallelASPJacobiGivensHouseholder/ B0290H Linear algebra (numerical analysis) C4140 Linear algebra (numerical analysis)An "alternating sequential-parallel" system (ASP) is introduced, and its ...