Problém nejmenších čtverc· (dále jen LS problém) je aproximační úloha řešení soustav lineárních algebraických rovnic, které jsou z nějakého d·vodu za- tíženy chybami. Existence a jednoznačnost řešení a metody řešení jsou známé pro r·zné typy matic, kterými tyto soustavy reprezentujeme. Typicky jsou ma- tice řídké a obrovských dimenzí, ale velmi často dostáváme z praxe i úlohy s maticemi o proměnlivé hustotě nenulových prvk·. Těmi se myslí řídké matice s jedním nebo více hustými řádky. Zde rozebíráme metody řešení tohoto LS pro- blému. Obvykle jsou založeny na rozdělení úlohy na hustou a řídkou část, které řeší odděleně. Tak pro řídkou část m·že přestat platit předpoklad plné sloupcové hodnosti, který je potřebný pro většinu metod. Proto se zde speciálně zabýváme postupy, které tento problém řeší. 1

In Paper [I] we use data on Swedish public procurement auctions for internal regularcleaning service contracts to provide novel empirical evidence regarding green publicprocurement (GPP) and its effect on the potential suppliers’ decision to submit a bid andtheir probability of being qualified for supplier selection. We find only a weak effect onsupplier behavior which suggests that GPP does not live up to its political expectations.However, several environmental criteria appear to be associated with increased complexity,as indicated by the reduced probability of a bid being qualified in the postqualificationprocess. As such, GPP appears to have limited or no potential to function as an environmentalpolicy instrument. In Paper [II] the observation is made that empirical evaluations of the effect of policiestransmitted through public procurements on bid sizes are made using linear regressionsor by more involved non-linear structural models. The aspiration is typically to determinea marginal effect. Here, I compare marginal effects generated under both types ofspecifications. I study how a political initiative to make firms less environmentally damagingimplemented through public procurement influences Swedish firms’ behavior. Thecollected evidence brings about a statistically as well as economically significant effect onfirms’ bids and costs. Paper [III] embarks by noting that auction theory suggests that as the number of bidders(competition) increases, the sizes of the participants’ bids decrease. An issue in theempirical literature on auctions is which measurement(s) of competition to use. Utilizinga dataset on public procurements containing measurements on both the actual and potentialnumber of bidders I find that a workhorse model of public procurements is bestfitted to data using only actual bidders as measurement for competition. Acknowledgingthat all measurements of competition may be erroneous, I propose an instrumental variableestimator that (given my data) brings about a competition effect bounded by thosegenerated by specifications using the actual and potential number of bidders, respectively.Also, some asymptotic results are provided for non-linear least squares estimatorsobtained from a dependent variable transformation model. Paper [VI] introduces a novel method to measure bidders’ costs (valuations) in descending(ascending) auctions. Based on two bounded rationality constraints bidders’costs (valuations) are given an imperfect measurements interpretation robust to behavioraldeviations from traditional rationality assumptions. Theory provides no guidanceas to the shape of the cost (valuation) distributions while empirical evidence suggeststhem to be positively skew. Consequently, a flexible distribution is employed in an imperfectmeasurements framework. An illustration of the proposed method on Swedishpublic procurement data is provided along with a comparison to a traditional BayesianNash Equilibrium approach.

Les composés électrochomes changent de couleur en fonction d'une tension qui leur est appliquée. La tenue en cyclage de couches minces à base de NiO, électrochrome cathodique, dépend fortement de la température et de la pression de dépôt. D’autre part la proportion de phase électrochimiquement active dépend fortement de l’épaisseur des couches. Selon le modèle proposé NiO en milieu KOH se transforme en hydroxyde de nickel Ni(OH)2 puis dans la phase de coloration en oxyhydroxyde NiOOH avant de revenir à sa forme réduite durant la phase décoloration. À la fin de ce cycle, des traces de phase colorée persistent. Nous avons développé des nouvelles méthodes numériques d’analyse des spectres d'absorption de rayons X, caractérisant la structure locale autour du nickel dans ces phases non cristallisées, afin de déterminer les concentrations des diverses espèces au cours du cycle. Aucune des méthodes habituellement pratiquées, comme la combinaison linéaire d’espèces modèles par la méthode des moindres carrés linéaire, et la méthode d’Analyse en Composantes Principales, ne sont adaptées aux cas de spectres fortement corrélés comme les oxydes-hydroxydes de nickel. Nous montrons qu’il est possible d’améliorer la méthode des moindres carrés en utilisant un algorithme original : « la méthode des Moindres Carrés Linéaire Progressive ». La base de cette méthode est fondée sur l’étude statistique des erreurs et corrélations. Ce travail a permis de valider le modèle électrochimique et d’évaluer pour la première fois la concentration en NiOOH dans la phase réduite, signature de l'irréversibilité. Seule, la présence avant cyclage de Ni(OH)2 dans les films de NiO n'a pu être expliquée / Electrochromic materials change their color versus an applied electric voltage. The electrochemical study of NiO thin films, which are cathodic electromic materials, shows an important oxidationreduction cycles lifetime dependance on thin films deposition temperature and pressure. The proportion of electrochemically active material depends on the film thickness. The proposed model suggests that in KOH NiO is transformed first to nickel hydroxide Ni(OH)2, and to nickel oxihydroxide in the coloration process, before returning to Ni(OH)2 in the decoloration step. At the end of the cycle, traces of the colored phase are still observed. We have developed a new X-Ray absorption spectroscopy numerical analysis method in order to characterize the concentration of each species present in these non crystalline materials. Mixed Ni oxides and hydroxides XAS spectra are highly correlated and Linear Least Squares and Principal Component Analysis methods proved to be totally inefficient. In order to improve the linear least squares method, we have developed a home-made algorithm named « Progressive Linear Least Squares method ». This method is based on the use of statistical errors and correlations evaluation of the spectra. It was then possible to valid the electrochemical model and to evaluate for the first time the concentration of residual NiOOH in the reduced thin film phases, related to the irreversibility of the electrochromic process. However, we were unable to explain the presence of a small amount of de Ni(OH)2 in the NiO films prepared at room temperature, prior to any electrochemical treatment

<p>This project investigates a laser radar system. The system is based on the principles of time-correlated single photon counting, and by measuring the times-of-flight of reflected photons it can find range profiles and perform three-dimensional imaging of scenes. Because of the photon counting technique the resolution and precision that the system can achieve is very high compared to analog systems. These properties make the system interesting for many military applications. For example, the system can be used to interrogate non-cooperative targets at a safe distance in order to gather intelligence. However, signal processing is needed in order to extract the information from the data acquired by the system. This project focuses on the analysis of different signal processing methods.</p><p>The Wiener filter and the Richardson-Lucy algorithm are used to deconvolve the data acquired by the photon counting system. In order to find the positions of potential targets different approaches of non-linear least squares methods are tested, as well as a more unconventional method called ESPRIT. The methods are evaluated based on their ability to resolve two targets separated by some known distance and the accuracy with which they calculate the position of a single target, as well as their robustness to noise and their computational burden.</p><p>Results show that fitting a curve made of a linear combination of asymmetric super-Gaussians to the data by a method of non-linear least squares manages to accurately resolve targets separated by 1.75 cm, which is the best result of all the methods tested. The accuracy for finding the position of a single target is similar between the methods but ESPRIT has a much faster computation time.</p>

This project investigates a laser radar system. The system is based on the principles of time-correlated single photon counting, and by measuring the times-of-flight of reflected photons it can find range profiles and perform three-dimensional imaging of scenes. Because of the photon counting technique the resolution and precision that the system can achieve is very high compared to analog systems. These properties make the system interesting for many military applications. For example, the system can be used to interrogate non-cooperative targets at a safe distance in order to gather intelligence. However, signal processing is needed in order to extract the information from the data acquired by the system. This project focuses on the analysis of different signal processing methods. The Wiener filter and the Richardson-Lucy algorithm are used to deconvolve the data acquired by the photon counting system. In order to find the positions of potential targets different approaches of non-linear least squares methods are tested, as well as a more unconventional method called ESPRIT. The methods are evaluated based on their ability to resolve two targets separated by some known distance and the accuracy with which they calculate the position of a single target, as well as their robustness to noise and their computational burden. Results show that fitting a curve made of a linear combination of asymmetric super-Gaussians to the data by a method of non-linear least squares manages to accurately resolve targets separated by 1.75 cm, which is the best result of all the methods tested. The accuracy for finding the position of a single target is similar between the methods but ESPRIT has a much faster computation time.