JuliaApproximation / JuliaApproximation/FastTransforms.jl
Why are second kind Chebyshev points the first kind extrema?
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- Dominant language
- Julia
- Stars
- 281
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- 27
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Description
julia> n = 10
10
julia> pts = chebyshevpoints(Float64, n+1, Val(2))
11-element FastTransforms.ChebyshevGrid{2, Float64}:
1.0
0.9510565162951536
0.8090169943749475
0.5877852522924731
0.30901699437494745
0.0
-0.30901699437494745
-0.5877852522924731
-0.8090169943749475
-0.9510565162951536
-1.0
julia> cos.(n.*acos.(pts))
11-element Vector{Float64}:
1.0
-1.0
1.0
-1.0
1.0
-1.0
1.0
-1.0
1.0
-1.0
1.0
Shouldn't they be the roots of the second kind Chebyshev polynomials?
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Research direction
Start by reproducing the Julia REPL example with chebyshevpoints(Float64, n+1, Val(2)) and cos.(n.*acos.(pts)). Read the definitions of the first- and second-kind Chebyshev points and polynomials, then determine whether the observed values are expected or indicate an implementation problem. Done means resolving the question with the relevant behavior or correction clearly identified.
Written by the indexing model from the issue text.
Assessment
- Tech stack
- julia
- Domain
- backend
- Issue type
- Bug
- Difficulty
- 4/5
- Estimated time
- 3-5 days
- Activity status
- Stale
- Clarity
- Needs clarification
- Newbie friendliness
- 25/100