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- Adlers, Mikael
(author)
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Topics in Sparse Least Squares Problems
- 2000
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Doctoral thesis (other academic/artistic)abstract
- This thesis addresses topics in sparse least squares computation. A stable method for solving the least squares problem, min ||Ax-b||2 is based on the QR factorization.Here we have addressed the difficulty for storing the orthogonal matrix Q. Using traditional methods, the number of nonzero elements in Q makes it in many cases not feasible to store. Using the multifrontal technique when computing the QR factorization,Q may be stored and used more efficiently. A new user friendly Matlab implementation is developed.When a row in A is dense the factor R from the QR factorization may be completely dense. Therefore problems with dense rows must be treated by special techniques. The usual way to handle dense rows is to partition the problem into one sparse and one dense subproblem. The drawback with this approach is that the sparse subproblem may be more ill-conditioned than the original problem or even not have a unique solution. Another method, useful for problems with few dense rows, is based on matrix stretching, where the dense rows are split into several less dense rows linked then together with new artificial variables. We give and analyze the conditioning of the matrix obtained by this method and show that no ill-conditioned subproblem arise.In many least squares problems upper and lower bounds on the variables have to be satisfied at the solution. This type of problem arises, for example, in reconstruction problems in geodesy and tomography. Here methods based on direct factorization methods for sparse matrix computation are explored. Two completely different approaches for solving the problem are discussed and compared, i.e. active set methods and primal-dual interior-point methods based on Mehrotra's predictor-corrector path following method. An active set block method suitable for sparse problems is developed and a convergence proof is presented. The choice of barrier parameter, multiple corrections and finite termination for the interior-point method are discussed. Numerical comparison is given of the active set method, the interior-point method, together with an trust region method based on the interior-reflective Newton implemented in the optimization toolbox for MATLAB. The numerical tests show that the block active set method is faster and gives better accuracy for both nondegenerate and degenerate problems.
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| 2. |
- Olstam, Johan, 1979-, et al.
(author)
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A Framework for Simulation of Surrounding Vehicles in Driving Simulators
- 2008
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In: ACM Transactions on Modeling and Computer Simulation. - : Association for Computing Machinery (ACM). - 1049-3301 .- 1558-1195. ; 18:3
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Journal article (peer-reviewed)abstract
- This article describes a framework for generation and simulation of surrounding vehicles in a driving simulator. The proposed framework generates a traffic stream, corresponding to a given target flow and simulates realistic interactions between vehicles. The framework is based on an approach in which only a limited area around the driving simulator vehicle is simulated. This closest neighborhood is divided into one inner area and two outer areas. Vehicles in the inner area are simulated according to a microscopic simulation model including advanced submodels for driving behavior while vehicles in the outer areas are updated according to a less time-consuming mesoscopic simulation model. The presented work includes a new framework for generating and simulating vehicles within a moving area. It also includes the development of an enhanced model for overtakings and a simple mesoscopic traffic model. The framework has been validated on the number of vehicles that catch up with the driving simulator vehicle and vice versa. The agreement is good for active and passive catch-ups on rural roads and for passive catch-ups on freeways, but less good for active catch-ups on freeways. The reason for this seems to be deficiencies in the utilized lane-changing model. It has been verified that the framework is able to achieve the target flow and that there is a gain in computational time of using the outer areas. The framework has also been tested within the VTI Driving simulator III.
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| 3. |
- Olstam, Johan, 1979-
(author)
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Simulation of Surrounding Vehicles in Driving Simulators
- 2009
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Doctoral thesis (other academic/artistic)abstract
- Driving simulators and microscopic traffic simulation are important tools for making evaluations of driving and traffic. A driving simulator is de-signed to imitate real driving and is used to conduct experiments on driver behavior. Traffic simulation is commonly used to evaluate the quality of service of different infrastructure designs. This thesis considers a different application of traffic simulation, namely the simulation of surrounding vehicles in driving simulators.The surrounding traffic is one of several factors that influence a driver's mental load and ability to drive a vehicle. The representation of the surrounding vehicles in a driving simulator plays an important role in the striving to create an illusion of real driving. If the illusion of real driving is not good enough, there is an risk that drivers will behave differently than in real world driving, implying that the results and conclusions reached from simulations may not be transferable to real driving.This thesis has two main objectives. The first objective is to develop a model for generating and simulating autonomous surrounding vehicles in a driving simulator. The approach used by the model developed is to only simulate the closest area of the driving simulator vehicle. This area is divided into one inner region and two outer regions. Vehicles in the inner region are simulated according to a microscopic model which includes sub-models for driving behavior, while vehicles in the outer regions are updated according to a less time-consuming mesoscopic model.The second objective is to develop an algorithm for combining autonomous vehicles and controlled events. Driving simulators are often used to study situations that rarely occur in the real traffic system. In order to create the same situations for each subject, the behavior of the surrounding vehicles has traditionally been strictly controlled. This often leads to less realistic surrounding traffic. The algorithm developed makes it possible to use autonomous traffic between the predefined controlled situations, and thereby get both realistic traffc and controlled events. The model and the algorithm developed have been implemented and tested in the VTI driving simulator with promising results.
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