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• W2080474146 abstract "Knowledge of a truncated Fourier series expansion for a discontinuous <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=2 pi> <mml:semantics> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>π<!-- π --></mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>2pi</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-periodic function, or a truncated Chebyshev series expansion for a discontinuous nonperiodic function defined on the interval <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-bracket negative 1 comma 1 right-bracket> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>[</mml:mo> <mml:mo>−<!-- − --></mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy=false>]</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>[-1, 1]</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, is used in this paper to accurately and efficiently reconstruct the corresponding discontinuous function. First an algebraic equation of degree <italic>M</italic> for the <italic>M</italic> locations of discontinuities in each period for a periodic function, or in the interval <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis negative 1 comma 1 right-parenthesis> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mo>−<!-- − --></mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>(-1, 1)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for a nonperiodic function, is constructed. The <italic>M</italic> coefficients in that algebraic equation of degree <italic>M</italic> are obtained by solving a linear algebraic system of equations determined by the coefficients in the known truncated expansion. By solving an additional linear algebraic system for the <italic>M</italic> jumps of the function at the calculated discontinuity locations, we are able to reconstruct the discontinuous function as a linear combination of step functions and a continuous function." @default.
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• W2080474146 date "1993-01-01" @default.
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• W2080474146 title "Accurate and efficient reconstruction of discontinuous functions from truncated series expansions" @default.
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• W2080474146 doi "https://doi.org/10.1090/s0025-5718-1993-1195430-1" @default.
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