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2011

Determinant Approximations

Ipsen, Ilse C. F., Lee, Dean J.

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A sequence of approximations for the determinant and its logarithm of a complex matrixis derived, along with relative error bounds.

The determinant approximations are derived from expansions of det(X)=exp(trace(log(X))), and they apply to non-Hermitian matrices.
Examples illustrate that these determinant approximations are efficient for lattice simulations of finite temperature nuclear matter, and that they use significantly less space than Gaussian elimination.
The first approximation in the sequence is a block diagonal approximation; it represents an extension of Fischer's and Hadamard's inequalities to non-Hermitian matrices.

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