• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.135-143
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• 2011

As a zero set of some multivariate splines, the piecewise algebraic variety is a kind of generalization of the classical algebraic variety. This paper presents an algorithm for isolating real roots of the zero-dimensional piecewise algebraic variety which is based on interval evaluation and the interval zeros of univariate interval polynomials in Bernstein form. An example is provided to show the proposed algorithm is effective.

• 대한수학회보
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• 제55권3호
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• pp.837-849
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• 2018

In this paper, we study the closedness such as seminomality and t-closedness, and Noetherian-like properties such as piecewise Noetherianness and Noetherian spectrum, of Hurwitz polynomial rings and Hurwitz series rings. To do so, we construct an isomorphism between a Hurwitz polynomial ring (resp., a Hurwitz series ring) and a factor ring of a polynomial ring (resp., a power series ring) in a countably infinite number of indeterminates.

• 대한수학회지
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• 제40권6호
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• pp.1075-1083
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• 2003

The purpose of this paper is to investigate the piecewise wise polynomial approximation for the curved boundary. We analyze the error of an approximated solution due to this approximation and then compare the approximation errors for the cases of polygonal and piecewise polynomial approximations for the curved boundary. Based on the results of analysis, p-version numerical methods for solving Dirichlet's problems are applied to any smooth curved domain.

• 대한수학회지
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• 제53권3호
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• pp.623-643
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• 2016

In this paper, we study piecewise Noetherian (resp., piecewise w-Noetherian) properties in several settings including flat (resp., t-flat) overrings, Nagata rings, integral domains of finite character (resp., w-finite character), pullbacks of a certain type, polynomial rings, and D + XK[X] constructions.

• Journal of information and communication convergence engineering
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• 제6권3호
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• pp.320-322
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• 2008

We present efficient algorithms for solving the piecewise-cubic approximation problems in the plane. Given a set D of n points in the plane, we find a piecewise-cubic polynomial curve passing through only the points of a subset S of D and approximating the other points using the uniform metric. The goal is to minimize the size of S for a given error tolerance $\varepsilon$, called the min-# problem, or to minimize the error tolerance $\varepsilon$ for a given size of S, called the min-$\varepsilon$ problem. We give algorithms with running times O($n^2$ logn) and O($n^3$) for both problems, respectively.

• Bulletin of the Korean Chemical Society
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• 제24권7호
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• pp.967-970
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• 2003

A new modified singular value decomposition method, piecewise polynomial truncated SVD (PPTSVD), which was originally developed to identify discontinuity of the earth's radial density function, has been used for large solvent peak suppression and noise elimination in nuclear magnetic resonance (NMR) signal processing. PPTSVD consists of two algorithms of truncated SVD (TSVD) and L₁ problems. In TSVD, some unwanted large solvent peaks and noise are suppressed with a certain soft threshold value, whereas signal and noise in raw data are resolved and eliminated in L₁ problems. These two algorithms were systematically programmed to produce high quality of NMR spectra, including a better solvent peak suppression with good spectral line shapes and better noise suppression with a higher signal to noise ratio value up to 27% spectral enhancement, which is applicable to multidimensional NMR data processing.

• ETRI Journal
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• 제6권2호
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• pp.18-26
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• 1984

Among the various forms of interpolating polynomial for approximation, this paper is a study about the characteristics of piecewise Lagrange interpolating polynomials. And throughout the study, an attempt is made to construct the two-dimensional ap proximating function over Rectangular Grid and Triangular Grid by using the one-dim ensional interpolating polynomials.

• 대한수학회보
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• 제59권1호
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• pp.45-72
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• 2022

In this work, we study Bernstein-Walsh-type estimations for the derivative of an arbitrary algebraic polynomial in regions with piecewise smooth boundary without cusps of the complex plane. Also, estimates are given on the whole complex plane.

• 한국CDE학회논문집
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• 제5권3호
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• pp.276-284
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• 2000

Usual practice of the transformation of a B-spline curve into a set of piecewise polynomial curves in a power form is done by either a knot refinement followed by basis conversions or applying a Taylor expansion on the B-spline curve for each knot span. Presented in this paper is a new algorithm, called a direct expansion algorithm, for the problem. The algorithm first locates the coefficients of all the linear terms that make up the basis functions in a knot span, and then the algorithm directly obtains the power form representation of basis functions by expanding the summation of products of appropriate linear terms. Then, a polynomial segment of a knot span can be easily obtained by the summation of products of the basis functions within the knot span with corresponding control points. Repeating this operation for each knot span, all of the polynomials of the B-spline curve can be transformed into a power form. The algorithm has been applied to both static and dynamic curves. It turns out that the proposed algorithm outperforms the existing algorithms for the conversion for both types of curves. Especially, the proposed algorithm shows significantly fast performance for the dynamic curves.

• 한국정보과학회논문지:시스템및이론
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• 제36권1호
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• pp.21-25
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• 2009

본 논문에서 우리는 평면상에 점들이 주어지는 경우에, 조각적 이차 다항식 곡선으로 맞추는 문제를 다룬다. 곡선은 이차 다항식 선분들로 이루어지고, 하나의 선분은 두 점 사이를 연결한다. 하지만 이 곡선은 점들의 부분집합만을 지나고, 지나지 못하는 점들에 대해서는 $L^{\infty}$거리로 에러를 측정한다. 이 문제에 대해서 우리는 두 가지 최적화 문제를 생각한다. 첫째로 허용 가능한 에러의 범위가 주어지고, 곡선 선분의 개수를 줄이는 문제이고, 둘째로 선분의 개수가 주어지고, 에러를 줄이는 문제이다. 주어진 점들의 개수 n에 대해서, 우리는 첫번째 문제에 대한 $O(n^2)$ 알고리즘과 두번째 문제에 대한 $O(n^3)$ 알고리즘을 제안한다.