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Chains of Recurrences  a method to expedite the evaluation of closedform functions
 In International Symposium on Symbolic and Algebraic Computing
, 1994
"... Chains of Recurrences (CR's) are introduced as an effective method to evaluate functions at regular intervals. Algebraic properties of CR's are examined and an algorithm that constructs a CR for a given function is explained. Finally, an implementation of the method in MAXIMA/Common Lisp i ..."
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Cited by 39 (7 self)
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is discussed. 1 Introduction Given a closedform function G(x), a common computational task is to evaluate the function at a number of points in an interval. More precisely, given a starting point x0 and an increment h, the task is to compute G(x0 + ih) for i = 0; 1; : : : ; n \Gamma 1. Such computations
Chains of Recurrences  a method to expedite the evaluation of closedform functions
 In International Symposium on Symbolic and Algebraic Computing
, 1994
"... Chains of Recurrences (CR's) are introduced as an effective method to evaluate functions at regular intervals. Algebraic properties of CR's are examined and an algorithm that constructs a CR for a given function is explained. Finally, an implementation of the method in MAXIMA/Common Lisp i ..."
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is discussed. 1 Introduction Given a closedform function G(x), a common computational task is to evaluate the function at a number of points in an interval. More precisely, given a starting point x0 and an increment h, the task is to compute G(x0 + ih) for i = 0; 1; : : : ; n \Gamma 1. Such computations
Sums of Closed Form Functions Satisfy Recurrence Relations
, 1991
"... We give a short, selfcontained proof of the fact that sums of closed form (hypergeometric) functions satisfy recurrence relations with polynomial coefficients. We obtain explicit bounds for the order of the recurrence and for the degrees of the coefficient polynomials directly from the form of the ..."
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Cited by 2 (0 self)
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We give a short, selfcontained proof of the fact that sums of closed form (hypergeometric) functions satisfy recurrence relations with polynomial coefficients. We obtain explicit bounds for the order of the recurrence and for the degrees of the coefficient polynomials directly from the form
A closedform solution for options with stochastic volatility with applications to bond and currency options
 Review of Financial Studies
, 1993
"... I use a new technique to derive a closedform solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and spotasset returns. I introduce stochastic interest rates and show how to apply the model to bond option ..."
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Cited by 1512 (6 self)
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I use a new technique to derive a closedform solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and spotasset returns. I introduce stochastic interest rates and show how to apply the model to bond
ICOLLIDE: An interactive and exact collision detection system for largescale environments
 In Proc. of ACM Interactive 3D Graphics Conference
, 1995
"... We present an exact and interactive collision detection system, ICOLLIDE, for largescale environments. Such environments are characterized by the number of objects undergoing rigid motion and the complexity of the models. The algorithm does not assume the objects ’ motions can be expressed as a c ..."
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Cited by 322 (24 self)
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closed form function of time. The collision detection system is general and can be easily interfaced with a variety of applications. The algorithm uses a twolevel approach based on pruning multipleobject pairs using bounding boxes and performing exact collision detection between selected pairs
A ClosedForm Solution to Natural Image Matting
 IEEE TRANS. PAMI
, 2008
"... Interactive digital matting, the process of extracting a foreground object from an image based on limited user input, is an important task in image and video editing. From a computer vision perspective, this task is extremely challenging because it is massively illposed—at each pixel we must estim ..."
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Cited by 136 (2 self)
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, or perform iterative nonlinear estimation by alternating foreground and background color estimation with alpha estimation. In this paper, we present a closedform solution to natural image matting. We derive a cost function from local smoothness assumptions on foreground and background colors and show
ClosedForm SpecifiedFuel Commands for On–Off Thrusters
"... A procedure is presented for generating on–off thruster commands for resttorest slewing of flexible systems. The command profiles induce a low level of residual vibration and can be designed to use any desired amount of thruster fuel. A key advantage of the proposed method is that the commands are ..."
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are described by closedform functions of the system parameters and the desired move distance. Performance measures such as maneuver speed, maximum transient deflection, and robustness to modeling errors indicate that the commands are attractive alternatives to time/fuel optimal commands that must be determined
Closedform likelihood expansions for multivariate diffusions
, 2008
"... This paper provides closedform expansions for the loglikelihood function of multivariate diffusions sampled at discrete time intervals. The coefficients of the expansion are calculated explicitly by exploiting the special structure afforded by the diffusion model. Examples of interest in financial ..."
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Cited by 109 (3 self)
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This paper provides closedform expansions for the loglikelihood function of multivariate diffusions sampled at discrete time intervals. The coefficients of the expansion are calculated explicitly by exploiting the special structure afforded by the diffusion model. Examples of interest
Closedform upper bounds in . . .
, 2011
"... The classical approach to automatic cost analysis consists of two phases. Given a program and some measure of cost, the analysis first produces cost relations (CRs), i.e., recursive equations which capture the cost of the program in terms of the size of its input data. Second, CRs are converted in ..."
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into closedform, i.e., without recurrences. Whereas the first phase has received considerable attention, with a number of cost analyses available for a variety of programming languages, the second phase has been comparatively less studied. This article presents, to our knowledge, the first practical
A note on the closedform identification of regression models with a mismeasured binary regressor.
 Statistics and Probability Letters
, 2008
"... Abstract This note considers the identification of a nonparametric regression model with an unobserved 01 dichotomous regressor. The sample consists of a dependent variable and a 01 dichotomous proxy of the unobserved regressor. We obtain nonparametric identification of every element in the model ..."
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Cited by 2 (0 self)
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in the model as a closedform function of the observed moments or densities. Our identification strategy does not require any additional sample information, such as instrumental variables or a secondary sample. The closedform solution may be used to construct estimators of the unknowns.
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