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Parallel algorithm for the eigenvalues and eigenvectors of a general matrix

Gautam Shroff

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Abstract

A new parallel Jacobi-like algorithm for computing the eigenvalues of a general complex matrix is presented. The asymptotic convergence rate of this algorithm is provably quadratic and this is also demonstrated in numerical experiments. The algorithm promises to be suitable for real-time signal processing applications. In particular the algorithm can be implemented using n2/4 processors taking O(n log2 n) time for random matrices.

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What this paper is about

A new parallel Jacobi-like algorithm for computing the eigenvalues of a general complex matrix is presented. The asymptotic convergence rate of this algorithm is provably quadratic and this is also demonstrated in numerical experiments. The algorithm promises to be suitable for real-time signal processing applications. In particular the algorithm can be implemented using n2/4 processors taking O(n log2 n) time for random matrices.

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Available abstract

A new parallel Jacobi-like algorithm for computing the eigenvalues of a general complex matrix is presented. The asymptotic convergence rate of this algorithm is provably quadratic and this is also demonstrated in numerical experiments. The algorithm promises to be suitable for real-time signal processing applications. In particular the algorithm can be implemented using n2/4 processors taking O(n log2 n) time for random matrices.

Key concepts: Eigenvalues and eigenvectors, Rate of convergence, Algorithm, Convergence (economics), Matrix (chemical analysis), Mathematics, Symmetric matrix, Quadratic equation

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