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We prove a general theorem providing smoothed analysis estimates for conic condition numbers of problems of numerical analysis. Our probability estimates depend only on geometric invariants of the corresponding sets of ill-posed inputs. Several applications to linear and polynomial equation solving show that the estimates obtained in this way are easy to derive and quite accurate. The main theorem is based on a volume estimate of \epsilon-tubular neighborhoods around a real algebraic subvarietydoi:10.1090/s0025-5718-08-02060-7 fatcat:evzix4if55ax5ft6hf3354z2w4