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High Accuracy Algorithms for Approximation of Discontinuity Lines of a Noisy Function
Proceedings of the Steklov Institute of Mathematics, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ageev, A. L., Antonova, T. V.
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Local Function Approximation in Evolutionary Algorithms for the Optimization of Costly Functions
IEEE Transactions on Evolutionary Computation, 2004We develop an approach for the optimization of continuous costly functions that uses a space-filling experimental design and local function approximation to reduce the number of function evaluations in an evolutionary algorithm. Our approach is to estimate the objective function value of an offspring by fitting a function approximation model over the k
R.G. Regis, C.A. Shoemaker
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An optimal adaptive algorithm for the approximation of concave functions
Mathematical Programming, 2005Consider a proper concave function \(f:[ 0,1] \to\mathbb R\), normalized so that \(f( 0) =0\) and \(f( 1) =1.\) \ Denote by \(f^{\prime }( \overline{x}) \) an arbitrary supergradient \(\xi \) of \(f\) at \(\overline{x},\) i.e., a supergradient \(\xi \) satisfying: \[ f( x) \leq f( \overline{x}) +\xi ( x-\overline{x} ) \text{ for all }x\in [ 0,1] \] Let
Guérin, J., Marcotte, P., Savard, G.
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ALGORITHM FOR CALCULATING FUNCTIONS IN METHOD OF SUCCESSIVE APPROXIMATIONS
International Journal of Modern Physics B, 1989A new algorithm is proposed for constructing unknown functions with the help of their several approximate expressions. The algorithm is illustrated by calculating the ground-state energy of anharmonic oscillator. Different variants of the method are analysed, and it is shown that the accuracy of the calculations can be carried to 0.1%.
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An Algorithm for the Automatic Approximate Minimization of Boolean Functions
IEEE Transactions on Computers, 1968Abstract—There are several algorithms that determine directly an irredundant normal form (INF) of a Boolean function without generating the entire set of prime implicants. These algorithms can generate solutions for the minimization problem much more rapidly than the algorithms determining minimum normal forms (MNF), and the cost of these solutions is,
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An improved algorithm for rational approximation of transfer functions
International Journal of Circuit Theory and Applications, 1977AbstractThe calculation of a rational transfer function is considered using a Laguerre expansion of the impulse response. An algorithm is proposed that avoids the appearance of high‐order surplus factors. Results of computer experiments are presented.
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A Randomized Algorithm for Weighted Approximation of Points by a Step Function
Discrete Mathematics, Algorithms and Applications, 2010The problem considered in this paper is: Given an integer k > 0 and a set P of n points in the plane each with a corresponding nonnegative weight, find a step function f with k steps that minimize the maximum weighted vertical distance between f and all the points in P.
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IEEE 1991 Ultrasonics Symposium, 2002
The problem of delay equalization in the design of SAW transducer weighting functions is considered. The need arises for an approach to the synthesis of finite impulse response functions with an arbitrary complex frequency response. Of late, several algorithms have been presented.
Richie, S. M., Abbott, B. P.
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The problem of delay equalization in the design of SAW transducer weighting functions is considered. The need arises for an approach to the synthesis of finite impulse response functions with an arbitrary complex frequency response. Of late, several algorithms have been presented.
Richie, S. M., Abbott, B. P.
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Systolic algorithm for multivariable approximation using tensor products of basis functions
Parallel Computing, 1991The paper is concerned with the approximation of \(f(x,y)\) by a function of the form \(\Omega(x,y)=\sum^ m_{i=1}\sum^ n_{j=1}a_{ij}\phi_ i(x)\psi_ j(y)\) which interpolates \(f\) at the rectangular grid of points \(\{(x_ i,y_ j)\}\). The authors discuss the choice of the basis functions \(\{\phi_ i(x)\}\), \(\{\psi_ j(y)\}\) and present a systolic ...
Krishnamurthy, E. V., Schröder, H.
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Two Algorithms for Piecewise-Linear Continuous Approximation of Functions of One Variable
IEEE Transactions on Computers, 1974Two simple heuristic algorithms for piecewise-linear approximation of functions of one variable are described. Both use a limit on the absolute value of error and strive to minimize the number of approximating segnents subject to the error limit. The first algorithm is faster and gives satisfactory results for sufficiently smooth functions.
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