A catalogue of algorithms for approximation

Grosse, E. H.

doi:10.1007/978-1-4899-3442-0_41

Cited by 17 publications

(7 citation statements)

References 367 publications

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“…(2) ckp = fin.v(bread, fgold)* (5) Because of the constant setting f = fgold, the dimension of fi,, : R 2 -R can be reduced to f/,,: R -R, by writing ckp = finv(Vbread)* (6) It is known that a higher ckp leads to a darker toast (higher f). Thus, c,ig,, of eq.…”

Section: Project Motivationmentioning

confidence: 99%

“…For simplicity u can be treated as being constant over time. 2 At the very beginning instead of the unknown u an initial estimate fi(0) is proposed. This initial estimate fi(0) may be any vector with fii e U,V i e {1... n} and might be a very bad estimate of u.…”

Section: Update-smoothing or Query-smoothingmentioning

confidence: 99%

“…the heights of the surface f(ji) [1]. Most of the methods allow noisy measurements of f(~i) [2,3,4,5,6,7,8,9]. The problem solved in these papers is to reconstruct the hypersurface from the set of sparse data points.…”

Section: Introductionmentioning

confidence: 99%

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Inverse passive learning of an input-output-map through update-spline-smoothing

Heiss

1994

IEEE Trans. Automat. Contr.

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This paper presents a robust method of learning passively a one-dimensional input-output-map when receiving only indirect information about the correct input-output-mlap (e.g. only the sign of the deviation between the actual estimated output value and the correct output value is obtained). This information is obtained for only one input-output combination per updating-cycle.The approach is to increment or decrement step by step the output values of the actually stored map and then to apply global or local cubic spline smoothing, in order to avoid "adaptation holes" at points which are never updated or less frequently updated than other points. This method works with noisy measurements as well as slowly timne-varying systems. Even discontinuous changes of the desired input-output-relation do not result in instability.Problems of convergence and stability are treated and design rules are given. Abstract This paper presents a robust method of learning passively a one-dimensional input-output-map when receiving only indirect information about the correct input-output-map (e.g. only the sign of the deviation between the actual estimated output value and the correct output value is obtained). This information is obtained for only one input-output combination per updating-cycle.The approach is to increment or decrement step by step the output values of the actually stored map and then to apply global or local cubic spline smoothing, in order to avoid "adaptation holes" at points which are never updated or less frequently updated than other points. This method works with noisy measurements as well as slowly time-varying systems. Even discontinuous changes of the desired input-output-relation do not result in instability.Problems of convergence and stability are treated and design rules are given.

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Section: Project Motivationmentioning

confidence: 99%

Section: Update-smoothing or Query-smoothingmentioning

confidence: 99%

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Inverse passive learning of an input-output-map through update-spline-smoothing

Heiss

1994

IEEE Trans. Automat. Contr.

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“…A large number of the above approaches, but this is not exhaustive, are documented in Grosse's catalog [12].…”

Section: Introductionmentioning

confidence: 99%

A Simple and Accurate Algorithm for Barycentric Rational Interpolation

Knockaert

2008

IEEE Signal Process. Lett.

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“…The equidistribution approach is described in White [12], and references therein, Kautsky and Nichols [9], Carey and Dinh [6], and Pryce [11]. A comprehensive up-to-date bibliography is given in Grosse [8].…”

Section: Introductionmentioning

confidence: 99%

Algorithms for optimal discontinuous piecewise linear and constant 𝐿₂ fits to continuous functions with adjustable nodes in one and two dimensions

Baines¹

1994

Math. Comp.

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Abstract. In this paper a direct variational approach (with nonstandard variations) is used to generate algorithms to determine optimal discontinuous piecewise linear and piecewise constant L2 fits to a continuous function of one or two variables with adjustable nodes. In the one-variable case the algorithm is fast and robust, the mesh cannot tangle, and the resulting fits are continuous a.e. In the two-variable case, on an adjustable triangular grid, the algorithm is less robust but gives good results for particular functions possessing a single steep feature. The extension to higher dimensions is straightforward.

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A catalogue of algorithms for approximation

Cited by 17 publications

References 367 publications

Inverse passive learning of an input-output-map through update-spline-smoothing

Inverse passive learning of an input-output-map through update-spline-smoothing

A Simple and Accurate Algorithm for Barycentric Rational Interpolation

Algorithms for optimal discontinuous piecewise linear and constant 𝐿₂ fits to continuous functions with adjustable nodes in one and two dimensions

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