Fast-Fourier least-squares

The method was successfully applied to insulin [125] and actinidin [139] and a number of other proteins [126]. For insulin, the final R for 1.5 A resolution was 0.11 for some 1077 atoms and 11 890 reflections. For actinidin, the final R for 10-1.7 A resolution was 0.17 for some 1821 atoms and 23390 reflections. The standard deviation in bond lengths from ideal values was 0.014 A. 

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Baker EN, Dodson EN (1980) Crystallographic refinement of the structure of actinidin at 1.7 A resolution by fast-Fourier least-squares methods. Acta Cryst A 36 559-572... 

Isaacs NW, Agarwal RC (1978) Experience with fast Fourier least squares in the refinement of the crystal structure of rhombohedral 2-Zn insulin at 1.5 A resolution. Acta Cryst A34 782-791... 

The most notable advance in computational crystallography was the availability of methods for rehning protein structures by least-squares optimization. This developed in a number of laboratories and was made feasible by the implementation of fast Fourier transform techniques [32]. The most widely used system was PROLSQ from the Flendrickson lab [33]. 

Finzel, B. C.( 1987). Incorporation of fast Fourier transforms to speed restrained least-squares refinement of protein structures. J. Appl. Crystallogr. 20,53-55. 

Figure 8. Dynamic mechanical spectrum (TBA) of Epon 828/PACM-20 in which the relative rigidity and logarithmic decrement have been calculated by four methods , peak-finding [PKF] , linear least squares (LSQ) +, non-linear least squares (NLSQ) and O, fast Fourier transform (FFT). For clarity the LSQ, NLSQ and FFT data have been displaced vertically in equal increments from the PKF data.

Many exercises also work in the earlier versions (1 through 4) of Excel. However, these earlier versions cannot handle VBA macros, so that those spreadsheet exercises that use macros for weighted least squares, fast Fourier transformation, and convolution, cannot be run with versions preceding Excel 5. (Specifically, these are exercises 3.4 and beyond in chapter 3, and all exercises in chapter 7.) Moreover, the macros described in chapter 10 cannot b e us ed in these earlier versions. 

GPS combined with gravity measurements The geoid determination and the height transfer across the Belt can also be based on gravity measurements. In the area of concern gravimetric measurement on land and sea have been performed in the past. Based on this data the Danish Geodetic Institute has carried out computations by Least-Squares Collocation (LSC) and by Fast Fourier Transform Method (FFT). A geoid, computed by the LSC... 

Konnert s technique for refining the structure of proteins subject to known geometrical constraints has been developed by incorporating restraints on the variances of the interatomic distributions, in order to express the retention of local geometry that accompanies certain modes of motion." As as alternative to the sparse matrix approach, Hoad and Norman have utilized the fast Gauss-Seidel least-squares routine for the refinement of atomic co-ordinates." A comparison has been made of the structures obtained for bovine trypsin (EC 3.4.24.4) by the difference Fourier and real space refinement methods." ... 

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