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  • 1
    Electronic Resource
    Electronic Resource
    Algebraic connections between the least squares and total least squares problems (1989)
    Springer
    Numerische Mathematik 55 (1989), S. 431-449 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 15A18 ; 65F20 CR: G1.3
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper the closeness of the total least squares (TLS) and the classical least squares (LS) problem is studied algebraically. Interesting algebraic connections between their solutions, their residuals, their corrections applied to data fitting and their approximate subspaces are proven. All these relationships point out the parameters which mainly determine the equivalences and differences between the two techniques. These parameters also lead to a better understanding of the differences in sensitivity between both approaches with respect to perturbations of the data. In particular, it is shown how the differences between both approaches increase when the equationsAX≈B become less compatible, when the length ofB orX is growing or whenA tends to be rank-deficient. They are maximal whenB is parallel with the singular vector ofA associated with its smallest singular value. Furthermore, it is shown how TLS leads to a weighted LS problem, and assumptions about the underlying perturbation model of both techniques are deduced. It is shown that many perturbation models correspond with the same TLS solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396047
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    The Curse of Scoreless Draws in Soccer: The Relationship with a Team's Offensive, Defensive, and Overall Performance (2008)
    Berkeley, Calif. : Berkeley Electronic Press (now: De Gruyter)
    Journal of quantitative analysis in sports 4 (2008), S. 4 
    Details
    ISSN: 1559-0410
    Source: Berkeley Electronic Press Academic Journals
    Topics: Sports Science
    Notes: In soccer, a scoreless draw is typically considered as an unwanted result that often jeopardizes the spectacle value of the game. In the present work, we tried to investigate a) how common scoreless draws are, and b) the relationship between scoreless draws and other indices of a football team's performance using machine learning techniques. Using data from 54 competitions around the world, Bayesian networks, least squares support vector machines and Hybrid Monte Carlo multi-layer perceptrons were used to investigate which combination of indices best predicts a team's season proportion of scoreless draws and to see exactly what predictions these indices make. There was ample variability in the proportion of scoreless draws, both when comparing individual teams and countries. For individual teams, the percentage scoreless draws varied between 0 and 30%. On average, nearly 9% of all games ended in 0-0. Not surprisingly, the most important parameter appeared to be the total number of goals per game. More interestingly, the earned points per game were also linked to the proportion of scoreless draws. Games of average and bad-to-average teams more often resulted in a scoreless draw, in particular when the games of these teams saw few goals. Such a team could end up having 20% scoreless draws in one season. A suggestive result that more spectators may be associated with less scoreless draws is also presented.
    Type of Medium: Electronic Resource
    URL: http://www.bepress.com/jqas/vol4/iss1/4
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  • 3
    Electronic Resource
    Electronic Resource
    Fast algorithm for solving the Hankel/Toeplitz Structured Total Least Squares problem (2000)
    Springer
    Numerical algorithms 23 (2000), S. 371-392 
    Details
    ISSN: 1572-9265
    Keywords: Hankel/Toeplitz matrix ; Structured Total Least Squares ; displacement rank ; 15A03 ; 62P30 ; 65F10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The Structured Total Least Squares (STLS) problem is a natural extension of the Total Least Squares (TLS) problem when constraints on the matrix structure need to be imposed. Similar to the ordinary TLS approach, the STLS approach can be used to determine the parameter vector of a linear model, given some noisy measurements. In many signal processing applications, the imposition of this matrix structure constraint is necessary for obtaining Maximum Likelihood (ML) estimates of the parameter vector. In this paper we consider the Toeplitz (Hankel) STLS problem (i.e., an STLS problem in which the Toeplitz (Hankel) structure needs to be preserved). A fast implementation of an algorithm for solving this frequently occurring STLS problem is proposed. The increased efficiency is obtained by exploiting the low displacement rank of the involved matrices and the sparsity of the associated generators. The fast implementation is compared to two other implementations of algorithms for solving the Toeplitz (Hankel) STLS problem. The comparison is carried out on a recently proposed speech compression scheme. The numerical results confirm the high efficiency of the newly proposed fast implementation: the straightforward implementations have a complexity of O((m+n)3) and O(m3) whereas the proposed implementation has a complexity of O(mn+n2).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019116520737
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    An efficient Total Least Squares algorithm based on a rank-revealing two-sided orthogonal decomposition (1993)
    Springer
    Numerical algorithms 4 (1993), S. 101-133 
    Details
    ISSN: 1572-9265
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Solving Total Least Squares (TLS) problemsAX≈B requires the computation of the noise subspace of the data matrix [A;B]. The widely used tool for doing this is the Singular Value Decomposition (SVD). However, the SVD has the drawback that it is computationally expensive. Therefore, we consider here a different so-called rank-revealing two-sided orthogonal decomposition which decomposes the matrix into a product of a unitary matrix, a triangular matrix and another unitary matrix in such a way that the effective rank of the matrix is obvious and at the same time the noise subspace is exhibited explicity. We show how this decompsition leads to an efficient and reliable TLS algorithm that can be parallelized in an efficient way.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02142742
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Efficient reduction algorithms for bordered band matrices (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 95-113 
    Details
    ISSN: 1070-5325
    Keywords: arrowhead matrix ; band matrix ; inverse eigenvalue problem ; givens rotations ; singular value decomposition ; updating ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Various plane rotation patterns are presented, which provide stable algorithms for reducing a b-band matrix bordered by p rows and/or columns to (b + p)-band form. These schemes generalize previously presented O(N2) reduction algorithms for matrices of order N, b = 1, and p = 1 to the reduction of more general b-band, p-bordered matrices where b ≥ 1 and p ≥ 1. Moreover, by splitting the matrix into two similarly structured submatrices and chasing nonzeros to the corners in two directions, the newly proposed patterns reduce the number of required rotations and hence the computational cost by one half compared to the other existing one-way chasing algorithms. Symmetric, as well as more general matrices, are considered. An example of the first type is the symmetric arrowhead matrix that arises in solving inverse eigenvalue problems. Examples of the second type are found in updating the singular value decomposition (SVD) and the partial SVD.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680020204
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  • 6
    Book
    Book
    Total least squares and errors-in-variables modeling / (2002)
    Dordrecht [u.a.] :Kluwer Academic Publ.,
    Details
    Title: Total least squares and errors-in-variables modeling /
    Contributer: Huffel, Sabine Van , International Workshop on Total Least Squares Techniques and Errors-in-Variables Modeling 〈3, 2001, Leuven〉 , International Workshop on TLS and EIV modeling 3 Leuven, Belgium 2001.08.27-29
    Publisher: Dordrecht [u.a.] :Kluwer Academic Publ.,
    Year of publication: 2002
    Pages: X, 397 S. : , Ill., Tab., graph. Darst.
    ISBN: 1-402-00476-1
    Type of Medium: Book
    Language: Undetermined
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