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David Zuckerman - One of the best experts on this subject based on the ideXlab platform.

  • robust fourier and Polynomial Curve fitting
    Foundations of Computer Science, 2016
    Co-Authors: Venkatesan Guruswami, David Zuckerman
    Abstract:

    We consider the robust Curve fitting problem, for both algebraic and Fourier (trigonometric) Polynomials, in the presence of outliers. In particular, we study the model of Arora and Khot (STOC 2002), who were motivated by applications in computer vision. In their model, the input data consists of ordered pairs (xi, yi) e [-1, 1] × [-1, 1], i = 1, 2, …, N, and there is an unknown degree-d Polynomial p such that for all but ρ fraction of the i, we have |p(xi) – yi|≤ δ. Unlike Arora-Khot, we also study the trigonometric setting, where the input is from T × [-1, 1], where T is the unit circle. In both scenarios, the i corresponding to errors are chosen randomly, and for such i the errors in the yi can be arbitrary. The goal is to output a degree-d Polynomial q such that ||p - q||∞ is small (for example, O(δ)). Arora and Khot could achieve a Polynomial-time algorithm only for ρ = 0. Daltrophe et al. observed that a simple median-based algorithm can correct errors if the desired accuracy δ is large enough. (Larger δ makes the output guarantee easier to achieve, which seems to typically outweigh the weaker input promise.) We dramatically expand the range of parameters for which recovery of q is possible in Polynomial time. Specifically, we show that there are Polynomial-time algorithms in both settings that recover q up to l∞ error O(δ.99) provided 1) ρ ≤/c1log d and δ ≥ 1/(log d)c, or 2) ρ ≤ c1/log log d/log2 d and δ ≥ 1/dc. Here c is any constant and c1 is a small enough constant depending on c. The number of points that suffices is N = O(d) in the trigonometric setting for random xi or arbitrary xi that are roughly equally spaced, or in the algebraic setting when the xi are chosen according to the Chebyshev distribution, and N = O(d2) in the algebraic setting with random (or roughly equally spaced) xi.

  • Robust Fourier and Polynomial Curve Fitting
    2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS), 2016
    Co-Authors: Venkatesan Guruswami, David Zuckerman
    Abstract:

    We consider the robust Curve fitting problem, for both algebraic and Fourier (trigonometric) Polynomials, in the presence of outliers. In particular, we study the model of Arora and Khot (STOC 2002), who were motivated by applications in computer vision. In their model, the input data consists of ordered pairs (xi, yi) ε [-1, 1] × [-1, 1], i = 1, 2,..., N, and there is an unknown degree-d Polynomial p such that for all but ρ fraction of the i, we have |p(xi) - yi|≤ δ. Unlike Arora-Khot, we also study the trigonometric setting, where the input is from T × [-1, 1], where T is the unit circle. In both scenarios, the i corresponding to errors are chosen randomly, and for such i the errors in the yi can be arbitrary. The goal is to output a degree-d Polynomial q such that ||p - q||∞ is small (for example, O(δ)). Arora and Khot could achieve a Polynomial-time algorithm only for ρ = 0. Daltrophe et al. observed that a simple median-based algorithm can correct errors if the desired accuracy δ is large enough. (Larger δ makes the output guarantee easier to achieve, which seems to typically outweigh the weaker input promise.) We dramatically expand the range of parameters for which recovery of q is possible in Polynomial time. Specifically, we show that there are Polynomial-time algorithms in both settings that recover q up to l∞ error O(δ.99) provided 1) ρ ≤/c1log d and δ ≥ 1/(log d)c, or 2) ρ ≤ c1/log log d/log2 d and δ ≥ 1/dc. Here c is any constant and c1 is a small enough constant depending on c. The number of points that suffices is N = Õ(d) in the trigonometric setting for random xi or arbitrary xi that are roughly equally spaced, or in the algebraic setting when the xi are chosen according to the Chebyshev distribution, and N = Õ(d2) in the algebraic setting with random (or roughly equally spaced) xi.

Mehrdad Hosseini Zadeh - One of the best experts on this subject based on the ideXlab platform.

  • VTC Fall - Automatic Vehicle Parallel Parking Design Using Fifth Degree Polynomial Path Planning
    2011 IEEE Vehicular Technology Conference (VTC Fall), 2011
    Co-Authors: Shuwen Zhang, Mehrdad Simkani, Mehrdad Hosseini Zadeh
    Abstract:

    Automatic vehicle parallel parking design and its related concerns about safety improvement remain some of the heated problems for automatic land vehicular control. This paper presents the calculation process of a parallel parking car's path planning and the algorithm development for its motion design based on a fifth-degree Polynomial Curve. In addition to the proposed algorithm for automatic vehicle parking, the minimum horizontal distance allowed for parking between a car and a parking spot is also investigated. The preliminary results show that the fifth degree Polynomial path planning and the algorithm are well applied to the automatic parallel parking problem.

  • Automatic Vehicle Parallel Parking Design Using Fifth Degree Polynomial Path Planning
    2011 IEEE Vehicular Technology Conference (VTC Fall), 2011
    Co-Authors: Shuwen Zhang, Mehrdad Simkani, Mehrdad Hosseini Zadeh
    Abstract:

    Automatic vehicle parallel parking design and its related concerns about safety improvement remain some of the heated problems for automatic land vehicular control. This paper presents the calculation process of a parallel parking car's path planning and the algorithm development for its motion design based on a fifth-degree Polynomial Curve. In addition to the proposed algorithm for automatic vehicle parking, the minimum horizontal distance allowed for parking between a car and a parking spot is also investigated. The preliminary results show that the fifth degree Polynomial path planning and the algorithm are well applied to the automatic parallel parking problem.

A C Cleland - One of the best experts on this subject based on the ideXlab platform.

  • Polynomial Curve fits for refrigerant thermodynamic properties extension to include r134a
    International Journal of Refrigeration-revue Internationale Du Froid, 1994
    Co-Authors: A C Cleland
    Abstract:

    Abstract Coefficients that extend previously published Polynomial Curve-fit equations thermodynamic properties of refrigerants to R134a are presented. The calculations are simple, and computationally fast; for commonly encountered refrigeration conditions predicted properties generally agree with the source data to within about ±0.4%, and differences of more than 0.6% occur only occasionally. This level of accuracy is satisfactory for applications such as dynamic simulation of refrigeration system performance in which some accuracy must be sacrificed in favour of computation speed. The coefficients to extend a simple empirical method for calculation of energy requirements for commercial and industrial refrigeration systems to R134a are also presented. The error in this simple method is less than 3% compared with full mass and energy balance calculations.

Venkatesan Guruswami - One of the best experts on this subject based on the ideXlab platform.

  • robust fourier and Polynomial Curve fitting
    Foundations of Computer Science, 2016
    Co-Authors: Venkatesan Guruswami, David Zuckerman
    Abstract:

    We consider the robust Curve fitting problem, for both algebraic and Fourier (trigonometric) Polynomials, in the presence of outliers. In particular, we study the model of Arora and Khot (STOC 2002), who were motivated by applications in computer vision. In their model, the input data consists of ordered pairs (xi, yi) e [-1, 1] × [-1, 1], i = 1, 2, …, N, and there is an unknown degree-d Polynomial p such that for all but ρ fraction of the i, we have |p(xi) – yi|≤ δ. Unlike Arora-Khot, we also study the trigonometric setting, where the input is from T × [-1, 1], where T is the unit circle. In both scenarios, the i corresponding to errors are chosen randomly, and for such i the errors in the yi can be arbitrary. The goal is to output a degree-d Polynomial q such that ||p - q||∞ is small (for example, O(δ)). Arora and Khot could achieve a Polynomial-time algorithm only for ρ = 0. Daltrophe et al. observed that a simple median-based algorithm can correct errors if the desired accuracy δ is large enough. (Larger δ makes the output guarantee easier to achieve, which seems to typically outweigh the weaker input promise.) We dramatically expand the range of parameters for which recovery of q is possible in Polynomial time. Specifically, we show that there are Polynomial-time algorithms in both settings that recover q up to l∞ error O(δ.99) provided 1) ρ ≤/c1log d and δ ≥ 1/(log d)c, or 2) ρ ≤ c1/log log d/log2 d and δ ≥ 1/dc. Here c is any constant and c1 is a small enough constant depending on c. The number of points that suffices is N = O(d) in the trigonometric setting for random xi or arbitrary xi that are roughly equally spaced, or in the algebraic setting when the xi are chosen according to the Chebyshev distribution, and N = O(d2) in the algebraic setting with random (or roughly equally spaced) xi.

  • Robust Fourier and Polynomial Curve Fitting
    2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS), 2016
    Co-Authors: Venkatesan Guruswami, David Zuckerman
    Abstract:

    We consider the robust Curve fitting problem, for both algebraic and Fourier (trigonometric) Polynomials, in the presence of outliers. In particular, we study the model of Arora and Khot (STOC 2002), who were motivated by applications in computer vision. In their model, the input data consists of ordered pairs (xi, yi) ε [-1, 1] × [-1, 1], i = 1, 2,..., N, and there is an unknown degree-d Polynomial p such that for all but ρ fraction of the i, we have |p(xi) - yi|≤ δ. Unlike Arora-Khot, we also study the trigonometric setting, where the input is from T × [-1, 1], where T is the unit circle. In both scenarios, the i corresponding to errors are chosen randomly, and for such i the errors in the yi can be arbitrary. The goal is to output a degree-d Polynomial q such that ||p - q||∞ is small (for example, O(δ)). Arora and Khot could achieve a Polynomial-time algorithm only for ρ = 0. Daltrophe et al. observed that a simple median-based algorithm can correct errors if the desired accuracy δ is large enough. (Larger δ makes the output guarantee easier to achieve, which seems to typically outweigh the weaker input promise.) We dramatically expand the range of parameters for which recovery of q is possible in Polynomial time. Specifically, we show that there are Polynomial-time algorithms in both settings that recover q up to l∞ error O(δ.99) provided 1) ρ ≤/c1log d and δ ≥ 1/(log d)c, or 2) ρ ≤ c1/log log d/log2 d and δ ≥ 1/dc. Here c is any constant and c1 is a small enough constant depending on c. The number of points that suffices is N = Õ(d) in the trigonometric setting for random xi or arbitrary xi that are roughly equally spaced, or in the algebraic setting when the xi are chosen according to the Chebyshev distribution, and N = Õ(d2) in the algebraic setting with random (or roughly equally spaced) xi.

Shuwen Zhang - One of the best experts on this subject based on the ideXlab platform.

  • VTC Fall - Automatic Vehicle Parallel Parking Design Using Fifth Degree Polynomial Path Planning
    2011 IEEE Vehicular Technology Conference (VTC Fall), 2011
    Co-Authors: Shuwen Zhang, Mehrdad Simkani, Mehrdad Hosseini Zadeh
    Abstract:

    Automatic vehicle parallel parking design and its related concerns about safety improvement remain some of the heated problems for automatic land vehicular control. This paper presents the calculation process of a parallel parking car's path planning and the algorithm development for its motion design based on a fifth-degree Polynomial Curve. In addition to the proposed algorithm for automatic vehicle parking, the minimum horizontal distance allowed for parking between a car and a parking spot is also investigated. The preliminary results show that the fifth degree Polynomial path planning and the algorithm are well applied to the automatic parallel parking problem.

  • Automatic Vehicle Parallel Parking Design Using Fifth Degree Polynomial Path Planning
    2011 IEEE Vehicular Technology Conference (VTC Fall), 2011
    Co-Authors: Shuwen Zhang, Mehrdad Simkani, Mehrdad Hosseini Zadeh
    Abstract:

    Automatic vehicle parallel parking design and its related concerns about safety improvement remain some of the heated problems for automatic land vehicular control. This paper presents the calculation process of a parallel parking car's path planning and the algorithm development for its motion design based on a fifth-degree Polynomial Curve. In addition to the proposed algorithm for automatic vehicle parking, the minimum horizontal distance allowed for parking between a car and a parking spot is also investigated. The preliminary results show that the fifth degree Polynomial path planning and the algorithm are well applied to the automatic parallel parking problem.