I. Bundles of Matrices and the Linear Independence of Their Minors: II. Applications of Laguerre's Method to the Matrix Eigenvalue Problem |
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abs ybar ALGOL ALGOL 60 ALPHA approximation arbitrary bundles B₁ B₂ basis vector BETA bool2 booll bundles are strictly Burroughs 220 calculate canonical form characteristic polynomial coefficients column complex convergence Correct Computed Criterion derivatives determinant determinantal ideals double precision eigenvalue problem eigenvectors eigsuml elementary divisors elements equation evaluation go to Hy GO TO L2 Hessenberg form Hessenberg matrix homogeneous Hyman's method imaginary initial vector inner product IROOT Laguerre iterates Laguerre's method lanczos Lemma linear linearly independent subset linearly independent t-minors lower Hessenberg multiple Newton iterate non-singular non-zero Note obtain OUTPUT pencils polynomials of degree precision number principal ideal ring Proof real roots regular bundles row j+1 RROOT set of determinantal single precision spur spur2 spurl step strictly equivalent superdiagonal tally Theorem tridiagonal form tridiagonal matrix Vj+1 xbar zero