By P. Ciarlini, M. G. Cox, F. Pavese, G. B. Rossi

This quantity collects refereed contributions according to the shows made on the 6th Workshop on complex Mathematical and Computational instruments in Metrology, held on the Istituto di Metrologia "G. Colonnetti" (IMGC), Torino, Italy, in September 2003. It offers a discussion board for metrologists, mathematicians and software program engineers that may inspire a more beneficial synthesis of talents, features and assets, and promotes collaboration within the context of ecu programmes, EUROMET and EA initiatives, and MRA requisites. It comprises articles via an incredible, around the world workforce of metrologists and mathematicians focused on dimension technological know-how and, including the 5 earlier volumes during this sequence, constitutes an authoritative resource for the mathematical, statistical and software program instruments essential to glossy metrology.

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**Example text**

These factorizations can be computed in a numerically stable way using a simple algorithm. For example, consider the factorization Equating terms we have tg2 = 2122, t 2 2 t 1 2 = v 1 2 and T11Tz = V11 - t 1 2 t T 2 . The problem is now reduced to finding the factorization of the modified 46 submatrix VII - t12tT2. The complete factorization can be achieved by repeating this step: I Set T ( i , j )= V ( i , j ) for , all i 2 j. I1 For k = n : -1 : 1, set T ( k ,k ) = T ( k ,k)1/2 and T(1:k-1,k) =T(l:k-l,k)/T(k,k).

For example, we have generated exact q for yj = 1, j = 1,.. 0],and then subtracted 10 from y2, simulating a discrepant value. Fig. 3 shows the perturbations y - q and corresponding i yi - qi f 2Uii associated with the input (first intervals yi - t ~ if 2 ~ i and + + 49 -. 04 I Figure 2. Residuals r = y - Ca along with error bars r izt2uii associated with the least squares fit t o the input data and f i f 20ii associated with the fit for the three adjusted uncertainties corresponding t o algorithms B, C and D.

Simple adjustment model To investigate adjustment procedures for determining estimates of the physical constants we consider a much simpler model involving five (fictitious) 48 6 . 64' 0 2 4 6 8 10 2 Figure 1. Input and adjusted uncertainties corresponding to procedures B, C, and D and for the 10 measurements of G. physical constants a = ( a ~ a2, , C Z ~ and ) ~ p = (PI, P 2 ) T and nine measurements with associated observation matrix -100 100 5 0 -5 100 -100 0 5 -5 100 0 100 -5 5 100 0 -100 -5 5 C= 0 100 100 5 -5 0 100 -100 5 5 5 0 0 100 100 0 0 -5 100 100 0 5 0 100 -100 The first six (last three) observations contain strong information about a (p).