Variations on the retraction algorithm for symmetric indefinite banded matrices Linda Kaufman

Standard B-K produces a bulge when pivoting for stabilityretract or prevent it. x x x x x x

x x x x x x x

x x x x x x x x

x x x x x x x x x r r r

x x x x x x x x x x r r

Use planar transformations to eliminate With block methods get 1) basic triangular shape 2) super long columns 3) short columns which don’t fit into rank k correction or vanish

x x x x x x x x x x x r

x x x x x x x x x x x

x x x x x x x x x x x

x x x x x x x x x x x

r x x x x x x x x x x x

r r x x x x x x x x x x

r r r x x x x x x x x x

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x x x x x x x x x x x x x x x x x x x x x x x x x x

x x y x y x wx wx x x

x x x z x q x q x x x x x x

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Variations on the retraction algorithm for symmetric ...

With block methods get. 1) basic triangular shape. 2) super long columns. 3) short columns which don't fit into rank k correction or vanish. x x x x x x. x x x x x x x. x x x x x x x x. x x x x x x x x x r r r. x x x x x x x x x x r r. x x x x x x x x x x x r. x x x x x x x x x x x. x x x x x x x x x x x. x x x x x x x x x x x r x x x x x x x x x x x.

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