On the Global Convergence of the Jacobi Method

Hari, Vjeran; Kovač, Erna Begović

doi:10.1002/pamm.201610351

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Computation Of Eigenvalues Of a Square1

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2021

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“…The proof of asymptotic quadratic convergence of the classic symmetric Jacobi method uses monotonicity of the offnorm, i.e., offnorm converges to a limit [14], [23], [24]. For the nonsymmetric case, the offnorm is no longer monotone.…”

Section: Computation Of Eigenvalues Of a Squarementioning

confidence: 99%

The Use of Solvable Directed Graphs in a Jacobi-like Algorithm

Turan

2021

EJMATH

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In this paper, we introduce a Jacobi-like algorithm (we call D-NJLA) to reduce a real nonsymmetric n × n matrix to a real upper triangular form by the help of solvable directed graphs. This method uses only real arithmetic and a sequence of orthogonal similarity transformations and achieves ultimate quadratic convergence. A theoretical analysis is constructed and some experimental results are given.

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Section: Computation Of Eigenvalues Of a Squarementioning

confidence: 99%