The quadratic approximation lemma and decompositions of superlative indexes

2002 ◽  
Vol 28 (1-2) ◽  
pp. 63-88 ◽  
Author(s):  
W. Erwin Diewert
Keyword(s):  
Quadratic Approximation ◽  
Approximation Lemma

scholarly journals Exact and inexact decompositions of trade price indices

2021 ◽  
Author(s):  
Andreas Benedictow ◽  
Pål Boug
Keyword(s):  
Quadratic Approximation ◽  
Clothing Industry ◽  
High Price ◽  
Average Price ◽  
Price Indices ◽  
First Order ◽  
Taylor Series Approximation ◽  
Market Shares ◽  
Approximation Lemma

AbstractA reasonable concept for the true trade price index in situations where low-price countries capture market shares from high-price countries is the average price paid by importers for the same quality of good or service from all exporting countries. However, decompositions of trade price indices are usually inexact in the sense that the average price used as the underlying aggregator formula is not exactly reproduced. In this paper, we compare analytically exact and inexact decompositions of trade price indices, paying particular attention to the bias in aggregate inflation occurring from applying the first-order Taylor series approximation and not the quadratic approximation lemma to a geometric average price. Our calculations, using the Norwegian clothing industry as an illustration, reveal that the bias in aggregate inflation over the sample period of 1997–2016 is quite substantial and as much as 0.6 percentage point in some years. We therefore conclude that the quadratic approximation lemma should be used in practice to exactly reproduce the underlying aggregator formula.

scholarly journals Continued fractions with low complexity: transcendence measures and quadratic approximation

2012 ◽  
Vol 148 (3) ◽  
pp. 718-750 ◽  
Author(s):  
Yann Bugeaud
Keyword(s):  
Lower Bound ◽  
Continued Fractions ◽  
Low Complexity ◽  
Quadratic Approximation ◽  
Real Numbers ◽  
Partial Quotients ◽  
Block Complexity

AbstractWe establish measures of non-quadraticity and transcendence measures for real numbers whose sequence of partial quotients has sublinear block complexity. The main new ingredient is an improvement of Liouville’s inequality giving a lower bound for the distance between two distinct quadratic real numbers. Furthermore, we discuss the gap between Mahler’s exponent w2 and Koksma’s exponent w*2.

scholarly journals Low-complexity feed-forward carrier phase estimation for M-ary QAM based on phase search acceleration by quadratic approximation

2015 ◽  
Vol 23 (15) ◽  
pp. 19142 ◽  
Author(s):  
Meng Xiang ◽  
Songnian Fu ◽  
Lei Deng ◽  
Ming Tang ◽  
Perry Shum ◽  
...  
Keyword(s):  
Carrier Phase ◽  
Low Complexity ◽  
Quadratic Approximation ◽  
Phase Estimation ◽  
Feed Forward

scholarly journals A novel fast Fourier transform accelerated off-grid exhaustive search method for cryo-electron microscopy fitting

2017 ◽  
Vol 50 (4) ◽  
pp. 1036-1047
Author(s):  
Alexandre Hoffmann ◽  
Valérie Perrier ◽  
Sergei Grudinin
Keyword(s):  
Electron Microscopy ◽  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Optimization Technique ◽  
Scoring Function ◽  
Trust Region ◽  
Search Method ◽  
Exhaustive Search ◽  
Quadratic Approximation ◽  
Cryo Electron Microscopy

This paper presents a novel fast Fourier transform (FFT)-based exhaustive search method extended to off-grid translational and rotational degrees of freedom. The method combines the advantages of the FFT-based exhaustive search, which samples all the conformations of a system under study on a grid, with a local optimization technique that guarantees to find the nearest optimal off-grid conformation. The method is demonstrated on a fitting problem and can be readily applied to a docking problem. The algorithm first samples a scoring function on a six-dimensional grid of sizeN6using the FFT. This operation has an asymptotic complexity ofO(N6logN). Then, the method performs the off-grid search using a local quadratic approximation of the cost function and the trust-region optimization algorithm. The computation of the quadratic approximation is also accelerated by FFT at the same additional asymptotic cost ofO(N6logN). The method is demonstrated by fitting atomic protein models into several simulated and experimental maps from cryo-electron microscopy. The method is available at https://team.inria.fr/nano-d/software/offgridfit.

A new piecewise quadratic approximation approach for L0 norm minimization problem

2018 ◽  
Vol 62 (1) ◽  
pp. 185-204 ◽  
Author(s):  
Qian Li ◽  
Yanqin Bai ◽  
Changjun Yu ◽  
Ya-xiang Yuan
Keyword(s):  
Minimization Problem ◽  
Quadratic Approximation ◽  
Approximation Approach ◽  
Norm Minimization
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