JSFH PERTURBATION ANALYSIS OF THE QR FACTOR R IN THE CONTEXT OF LLL LATTICE BASIS REDUCTION Xiao-Wen Chang, Damien Stehle and Gilles Villard This MAPLE work-sheet corresponds to the computations mentioned in Subsection 6.1 of the article. The goal is to explicit some constants hidden in [Higham02, Chapter 19], in the context of the backward stability of the Householder algorithm for computing the R factor of the QR factorization of a full-rank matrix, with standard floating-point arithmetic.JSFHJSFHJSFHJSFHNotation: u = 2^(-p).Assumption: 2n(6m+63) u <= 1 for variant A and 4n(6m+39) u <= 1 for variant B. Since we can take n >=2, this implies that 4 (6m+63) u <= 1 for variant A and8(6m+39) u <= 1 for variant B.JSFHJSFHJSFHJSFH******************************************************************************************* LEMMA 6.1: Delta v <= 2(m+6) u |v| **************************************************************************************************JSFHJSFHJSFH Eq. (6.2): the assumption implies (m+2) u < 1.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B0 < 1 <=> 2(m+2)u <1 <= Assumption.The bivariate series expansion of B0 has only non-negative terms. 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The bivariate series expansion of B1 has only non-negative terms. 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The bivariate series expansion of B2 has only non-negative terms. 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The bivariate series expansion of B3 has only non-negative terms. Thanks to the initial assumption, we have m.u <= 1/60. So we can replace each m by 1/(60*u). Also, since m can be assumed >=2, the initial assumption implies that each u is <= 1/(60*7).This provides an upper bound to B3 (used for C3, i.e., Eq. (6.9), see below).JSFHJSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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 bivariate series expansion of B4 has only non-negative terms. We bound B4 in the same fashion as we bounded B3.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 bivariate series expansion of B5 has only non-negative terms. We bound B5 in the same fashion as we bounded B3.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The bivariate series expansion of B6 has only non-negative terms. To bound B6, we compute the truncation of its series expansion around u=0 up to someprecision. We then upper bound the difference using the non-negativity of the coefficientsof the series expansion.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JSFHJSFHJSFHJSFHJSFHVARIANT B.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The bivariate series expansion of C3 has only non-negative terms. 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 bivariate series expansion of C4 has only non-negative terms. We bound C4 in the same fashion as we bounded B3.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The bivariate series expansion of C5 has only non-negative terms. We bound C5 in the same fashion as we bounded B3.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The bivariate series expansion of C6 has only non-negative terms. To bound C6, we compute the truncation of its series expansion around u=0 up to someprecision. We then upper bound the difference using the non-negativity of the coefficientsof the series expansion.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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******************************************************************************************* LEMMA 6.2: ||Delta Q||_F <= 15/2 (m+9) u **************************************************************************************************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 bivariate series expansion of B9 has only non-negative terms. 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 bivariate series expansion of C9 has only non-negative terms. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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JSFHJSFH