Search results
Results from the WOW.Com Content Network
Proof. Apply the Theorem to A T while recognizing that the eigenvalues of the transpose are the same as those of the original matrix. Example. For a diagonal matrix, the Gershgorin discs coincide with the spectrum. Conversely, if the Gershgorin discs coincide with the spectrum, the matrix is diagonal.
The Gershgorin circle theorem applies the companion matrix of the polynomial on a basis related to Lagrange interpolation to define discs centered at the interpolation points, each containing a root of the polynomial; see Durand–Kerner method § Root inclusion via Gerschgorin's circles for details.
Download as PDF; Printable version; ... Area of a circle; Area theorem (conformal mapping) ... Gershgorin circle theorem; Gibbs' inequality;
Gershgorin's circle theorem itself has a very short proof. A strictly diagonally dominant matrix (or an irreducibly diagonally dominant matrix [2]) is non-singular. A Hermitian diagonally dominant matrix with real non-negative diagonal entries is positive semidefinite. This follows from the eigenvalues being real, and Gershgorin's circle ...
Download as PDF; Printable version; ... Fundamental theorem of finitely generated abelian groups; G. Gershgorin circle theorem; H.
Geroch's splitting theorem (differential geometry) Gershgorin circle theorem (matrix theory) Gibbard–Satterthwaite theorem (voting methods) Girsanov's theorem (stochastic processes) Glaisher's theorem (number theory) Gleason's theorem (Hilbert space) Glivenko's theorem (mathematical logic) Glivenko's theorem (probability) Glivenko–Cantelli ...
Print/export Download as PDF; Printable version; In other projects Appearance. ... title=Gershgorin Circle Theorem}}): Gershgorin circle theorem;
Verification of nonlinear equations (The Kantorovich theorem, [34] Krawczyk method, interval Newton method, and the Durand–Kerner–Aberth method are studied.) Verification for solutions of ODEs, PDEs [35] (For PDEs, knowledge of functional analysis are used. [34]) Verification of linear programming [36] Verification of computational geometry