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Directionpreserving and Schurmonotonic semiseparable approximations of symmetric positive definite matrices
 SIAM J. Matrix Anal. Appl
"... Abstract. For a given symmetric positive definite matrix A ∈ R N×N, we develop a fast and backward stable algorithm to approximate A by a symmetric positive definite semiseparable matrix, accurate to a constant multiple of any prescribed tolerance. In addition, this algorithm preserves the product, ..."
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Cited by 2 (1 self)
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Abstract. For a given symmetric positive definite matrix A ∈ R N×N, we develop a fast and backward stable algorithm to approximate A by a symmetric positive definite semiseparable matrix, accurate to a constant multiple of any prescribed tolerance. In addition, this algorithm preserves the product
Bundle Adjustment  A Modern Synthesis
 VISION ALGORITHMS: THEORY AND PRACTICE, LNCS
, 2000
"... This paper is a survey of the theory and methods of photogrammetric bundle adjustment, aimed at potential implementors in the computer vision community. Bundle adjustment is the problem of refining a visual reconstruction to produce jointly optimal structure and viewing parameter estimates. Topics c ..."
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Cited by 555 (12 self)
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covered include: the choice of cost function and robustness; numerical optimization including sparse Newton methods, linearly convergent approximations, updating and recursive methods; gauge (datum) invariance; and quality control. The theory is developed for general robust cost functions rather than
Renormalization group flows from holography  Supersymmetry and a ctheorem
 ADV THEOR. MATH. PHYS
, 1999
"... We obtain first order equations that determine a supersymmetric kink solution in fivedimensional N = 8 gauged supergravity. The kink interpolates between an exterior antide Sitter region with maximal supersymmetry and an interior antide Sitter region with one quarter of the maximal supersymmetry. ..."
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Cited by 299 (25 self)
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sector of N = 2 gauge theories based on quiver diagrams. We consider more general kink geometries and construct a cfunction that is positive and monotonic if a weak energy condition holds in the bulk gravity theory. For evendimensional boundaries, the cfunction coincides with the trace anomaly
An Ensemble Adjustment Kalman Filter for Data Assimilation
, 2001
"... A theory for estimating the probability distribution of the state of a model given a set of observations exists. This nonlinear ..."
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Cited by 283 (12 self)
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A theory for estimating the probability distribution of the state of a model given a set of observations exists. This nonlinear
Riemannian geometry on positive definite matrices
, 2008
"... The Riemannian metric on the manifold of positive definite matrices is defined by a kernel function φ in the form K φ ∑ D (H, K) = i,j φ(λi, λj) −1Tr PiHPjK when ∑ i λiPi is the spectral decomposition of the foot point D and the Hermitian matrices H, K are tangent vectors. For such kernel metrics th ..."
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Cited by 4 (3 self)
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The Riemannian metric on the manifold of positive definite matrices is defined by a kernel function φ in the form K φ ∑ D (H, K) = i,j φ(λi, λj) −1Tr PiHPjK when ∑ i λiPi is the spectral decomposition of the foot point D and the Hermitian matrices H, K are tangent vectors. For such kernel metrics
SecondOrder Cone Programming
 MATHEMATICAL PROGRAMMING
, 2001
"... In this paper we survey the second order cone programming problem (SOCP). First we present several applications of the problem in various areas of engineering and robust optimization problems. We also give examples of optimization problems that can be cast as SOCPs. Next we review an algebraic struc ..."
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Cited by 231 (11 self)
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structure that is connected to SOCP. This algebra is a special case of a Euclidean Jordan algebra. After presenting duality theory, complementary slackness conditions, and definitions and algebraic characterizations of primal and dual nondegeneracy and strict complementarity we review the logarithmic
Results 1  10
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