In this article, the development of an autonomous robot trajectory generation system based on a single eye-in-hand webcam, where the workspace map is not known a priori, is described. The system makes use of image pro...
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ISBN:
(纸本)9780878492695
In this article, the development of an autonomous robot trajectory generation system based on a single eye-in-hand webcam, where the workspace map is not known a priori, is described. The system makes use of image processing methods to identify locations of obstacles within the workspace and the Quadtree Decomposition algorithm to generate collision free paths. The shortest path is then automatically chosen as the path to be traversed by the robot end-effector. The method was implemented using MATLAB running on a PC and tested on a two-link SCARA robotic arm. The tests were successful and indicate that the method could be feasibly implemented on many practical applications.
The definition, in previous studies, of vector Stieltjes continued fractions in connection with spectral properties of band operators with intermediate zero diagonals, left unsolved the question of a direct definition...
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The definition, in previous studies, of vector Stieltjes continued fractions in connection with spectral properties of band operators with intermediate zero diagonals, left unsolved the question of a direct definition of their coefficients in terms of the original data, a vector of Stieltjes series. The subject was more undefined in the matrix case. A new version of the qd algorithm for matrix problem, allows to extend to the vector and matrix cases the result of Stieltjes, expansion of a (scalar) function in terms of a Stielties continued fraction. Beside this connection, it solves the inverse Miura transform and gives interesting identities between general band matrix and sparse band matrix. Finally, as a consequence, we extend to some dynamical systems a method known for Toda lattices. (C) 2004 Published by Elsevier Inc.
Almost four decades passed after the discovery of solitons and infinite dimensional integrable systems. The theory of integrable systems has had great impact to wide area in physics and mathematics. In this paper an a...
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ISBN:
(纸本)0769521509
Almost four decades passed after the discovery of solitons and infinite dimensional integrable systems. The theory of integrable systems has had great impact to wide area in physics and mathematics. In this paper an approach to numerical algorithms in terms of integrable systems is surveyed. Some integrable systems of Lax form describe continuous flows of efficient numerical algorithms, for example, the QR algorithm and the Jacobi algorithm. Discretizations of integrable systems in tau-function level enable us to formulate algorithms for computing continued fractions such as the qd algorithm and the discrete Schur flow. A new singular value decomposition (I-SVD) algorithm is designed by using a discrete integrable system defined by the Christoffel-Darboux identity for orthogonal polynomials.
The epsilon algorithm is recommended as the best all-purpose acceleration method for slowly converging sequences. It exploits the numerical precision of the data to extrapolate the sequence to its limit. We explain it...
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The epsilon algorithm is recommended as the best all-purpose acceleration method for slowly converging sequences. It exploits the numerical precision of the data to extrapolate the sequence to its limit. We explain its connections with Pade approximation and continued fractions which underpin its theoretical base. Then we review the most recent extensions of these principles to treat application of the epsilon algorithm to vector-valued sequences, and some related topics. In this paper, we consider the class of methods based on using generalised inverses of vectors, and the formulation specifically includes the complex case wherever possible. (C) 2000 Elsevier Science B.V. All rights reserved.
The finite Toda molecule over finite fields is introduced whose dynamics are completely classified by conserved quantities. The trajectories blow up in a finite time or are periodic. A BCH-Goppa decoding algorithm is ...
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The finite Toda molecule over finite fields is introduced whose dynamics are completely classified by conserved quantities. The trajectories blow up in a finite time or are periodic. A BCH-Goppa decoding algorithm is designed. The number of Toda particles is congruent with the maximal number of errors to be decoded. (C) 1998 Elsevier Science B.V.
This paper is a continuation of Part I [M. H. Gutknecht, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 594–639], where the theory of the “unsymmetric” Lanczos biorthogonalization (BO) algorithm and the corresponding i...
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This paper is a continuation of Part I [M. H. Gutknecht, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 594–639], where the theory of the “unsymmetric” Lanczos biorthogonalization (BO) algorithm and the corresponding iterative method BIORES for non-Hermitian linear systems was extended to the nongeneric case. The analogous extension is obtained here for the biconjugate gradient (or BIOMIN) method and for the related BIODIR method. Here, too, the breakdowns of these methods can be cured. As a preparation, mixed recurrence formulas are derived for a pair of sequences of formal orthogonal polynomials belonging to two adjacent diagonals in a nonnormal Padé table, and a matrix interpretation of these recurrences is developed. This matrix interpretation leads directly to a completed formulation of the progressive qd algorithm, valid also in the case of a nonnormal Padé table. Finally, it is shown how the cure for exact breakdown can be extended to near-breakdown in such a way that (in exact arithmetic) the well-conditioned formal orthogonal polynomials and the corresponding Krylov space vectors do not depend on the threshold specifying the near-breakdown.
The theory of the "unsymmetric" Lanczos biorthogonalization (BO) algorithm, which has so far been restricted to an essentially generic situation (characterized by the nonsingularity of the leading principal ...
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The theory of the "unsymmetric" Lanczos biorthogonalization (BO) algorithm, which has so far been restricted to an essentially generic situation (characterized by the nonsingularity of the leading principal submatrices of the associated moment matrix or by the existence of a full set of regular formal orthogonal polynomials) is extended to the nongeneric case. The "serious" breakdowns due to the occurrence of two orthogonal right and left iteration vectors x(n) and y(n) can be overcome. For an operator of finite rank N the nongeneric BO algorithm, which generalizes the look-ahead Lanczos algorithm of Parlett, Taylor, and Liu [Math. Comp., 44 (1985), pp. 105-124], terminates regularly in at most N steps, except when a very special situation depending on the initial vectors occurs;but even then the algorithm produces in at most N steps a block tridiagonal matrix whose blocks are either small or sparse and whose characteristic polynomial is the minimal polynomial of the restriction of the operator to an invariant subspace. Formulas are also derived for a nongeneric version of the corresponding linear equation solver BIORES (brief for BIORTHORES or Lanczos/ORTHORES). The whole theory is developed as a consequence of known corresponding results on formal orthogonal polynomials and Pade approximants, for many of which new and simpler derivations are given.
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