From 1bd226e6cfcb82b0b83a117c802649fb1409615c Mon Sep 17 00:00:00 2001 From: MikaelSlevinsky Date: Fri, 1 Nov 2024 14:40:54 -0500 Subject: [PATCH] bits and bobs --- src/GramMatrix.jl | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/src/GramMatrix.jl b/src/GramMatrix.jl index 21017a2..1c2ee6c 100644 --- a/src/GramMatrix.jl +++ b/src/GramMatrix.jl @@ -7,7 +7,7 @@ abstract type AbstractGramMatrix{T} <: LayoutMatrix{T} end """ GramMatrix(W::AbstractMatrix, X::AbstractMatrix) -Construct a Gram matrix of size ``size(W)`` with data stored in ``W``. +Construct a symmetric positive-definite Gram matrix with data stored in ``W``. Given a family of orthogonal polynomials ``{\\bf P}(x) = \\{p_0(x), p_1(x),\\ldots\\}`` and a continuous inner product ``\\langle f, g\\rangle``, the Gram matrix is defined by: ```math @@ -161,7 +161,7 @@ end """ ChebyshevGramMatrix(μ::AbstractVector) -Construct a Chebyshev--Gram matrix of size ``(length(μ)+1)÷2`` with entries: +Construct a Chebyshev--Gram matrix of size `(length(μ)+1)÷2` with entries: ```math W_{i,j} = \\frac{\\mu_{|i-j|+1} +\\mu_{i+j-1}}{2}. ```