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Update GramMatrix.jl
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src/GramMatrix.jl

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@@ -55,8 +55,8 @@ GramMatrix(W::WT, X::XT) where {T, WT <: AbstractMatrix{T}, XT <: AbstractMatrix
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Construct a GramMatrix from modified orthogonal polynomial moments and the multiplication operator.
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In the standard (classical) normalization, ``p_0(x) = 1``, so that the moments
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``\\mu_n = ⟨ p_{n-1}, 1⟩`` are in fact the first column of the Gram matrix.
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The recurrence is built from ``X^\\top W = WX``.
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``µ_n = ⟨ p_{n-1}, 1⟩`` are in fact the first column of the Gram matrix.
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The recurrence is built from ``XᵀW = WX``.
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"""
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GramMatrix::AbstractVector{T}, X::XT) where {T, XT <: AbstractMatrix{T}} = GramMatrix(μ, X, one(T))
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function GramMatrix::AbstractVector{T}, X::XT, p0::T) where {T, XT <: AbstractMatrix{T}}
@@ -221,12 +221,12 @@ end
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Construct a Chebyshev--Gram matrix of size `(length(μ)+1)÷2` with entries:
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```math
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W_{i,j} = \\frac{\\mu_{|i-j|+1} +\\mu_{i+j-1}}{2}.
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W_{i,j} = \\frac{µ_{|i-j|+1} +µ_{i+j-1}}{2}.
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```
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Due to the linearization of a product of two first-kind Chebyshev polynomials,
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the Chebyshev--Gram matrix can be constructed from modified Chebyshev moments:
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```math
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\\mu_{n} = ⟨ T_{n-1}, 1⟩.
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µ_{n} = ⟨ T_{n-1}, 1⟩.
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```
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Specialized construction and Cholesky factorization is given for this type.
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