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In this paper, we study the problem of recovering the camera motion in a multiview setting given observation of tracked features in a three-dimensional environment. We propose a novel algorithm to simultaneously recover the pose (orientation and translation to within a scale) of every camera directly using a manifold optimization approach. Our contributions are four-fold. We present a new analytic...
This paper is concerned with a two-time-scale approximation of Wonham filters. A main feature is that the underlying hidden Markov chain has a large state space. To reduce computational complexity, we develop two-time-scale approach. Under time scale separation, we divide the state space of the Markov chain into a number of groups such that the chain jumps rapidly within each group and switches occasionally...
Self-concordant functions are a special class of convex functions introduced by Nesterov and Nemirovskii and used in interior point methods. This paper proposes a damped conjugate gradient method for optimization of self-concordant functions. This method is an ordinary conjugate gradient method but with a novel step-size selection rule which is proved to ensure the algorithm converges to the global...
A numerically stable homotopy continuation method was first proposed by Enqvist for computing degree constrained rational covariance extensions. The approach was later adapted in the works of Nagamune, and Blomqvist and Nagamune, to the Nevanlinna-Pick interpolation problem and more general complexity constrained problems. However, the method has not been developed to the fullest extent as all the...
Multinomial representations are derived for majority logic operations on bipolar binary data. The coefficients are given simply in terms of the readily computed lower Cholesky factor of Pascal matrices of order n for codes of block length n
This paper presents a new approach for solving balanced realization problems with emphasis on the time varying case. Instead of calculating the exact solutions for balancing at each time instant, we estimate with arbitrary accuracy the balancing solutions by means of Riccati equations associated with the balancing problems. Under uniform boundedness conditions on the controllability grammians and...
Recent work has shown that the algebraic question of determining the eigenvalues, or singular values, of a matrix can be answered by solving certain continuous-time gradient flows on matrix manifolds. To obtain computational methods based on this theory, it is necessary to develop recursive algorithms which achieve the same solutions as the continuous-time flows. In this paper we propose two recursive...
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