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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:application
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gptkb:Chebyshev_acceleration
gptkb:Chebyshev_expansion
gptkb:Chebyshev_iterative_method
gptkb:Chebyshev_matrix
gptkb:Chebyshev_pseudospectral_method
gptkb:Chebyshev_quadrature
gptkb:Chebyshev_rational_functions
gptkb:Chebyshev_series
gptkb:Chebyshev_spectral_method
gptkb:Chebyshev_transform
gptkb:Chebyshev_distance
gptkb:Chebyshev_filter
gptkb:Chebyshev_inequality
gptkb:Chebyshev_approximation
gptkb:Chebyshev_nodes
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gptkbp:category
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orthogonal polynomials
special functions
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gptkbp:definedIn
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interval [-1, 1]
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gptkbp:degree
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n
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gptkbp:explicitFormula
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T_n(x) = cos(n arccos(x))
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gptkbp:field
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gptkb:mathematics
numerical analysis
approximation theory
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gptkbp:firstPolynomial
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T_0(x) = 1
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https://www.w3.org/2000/01/rdf-schema#label
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Chebyshev polynomials
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gptkbp:minimumMaximumDeviation
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yes
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gptkbp:namedAfter
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gptkb:Pafnuty_Chebyshev
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gptkbp:orthogonalWithRespectTo
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weight function (1-x^2)^(-1/2)
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gptkbp:recurrence
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T_{n+1}(x) = 2x T_n(x) - T_{n-1}(x)
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gptkbp:relatedTo
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gptkb:Gegenbauer_polynomials
gptkb:Jacobi_polynomials
gptkb:Legendre_polynomials
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gptkbp:roots
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cos((2k-1)π/(2n)), k=1,...,n
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gptkbp:secondPolynomial
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T_1(x) = x
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gptkbp:sequence
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T_n(x)
U_n(x)
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gptkbp:symbol
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T_n(x)
U_n(x)
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gptkbp:type
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orthogonal polynomials
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gptkbp:usedIn
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gptkb:signal_processing
Fourier analysis
interpolation
numerical integration
filter design
minimax approximation
root finding
spectral methods
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gptkbp:bfsParent
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gptkb:Pafnuty_Chebyshev
gptkb:Hermite_polynomials
gptkb:ChebNet
gptkb:Sturm–Liouville_problem
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gptkbp:bfsLayer
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6
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