Approximate and Matrix-Free Equilibration

Mathematics – Numerical Analysis

Scientific paper

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Scientific paper

The condition number of a diagonally scaled matrix, for appropriately chosen scaling matrices, is often less than that of the original. Approximate equilibration scales a matrix so that the scaled matrix's row and column norms are approximately equal. We develop approximate equilibration algorithms for both nonsymmetric and symmetric matrices that access a matrix only by matrix-vector products, and we show that approximate equilibration is possible for all structurally nonsingular matrices.

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