Hermite approximations composed with adaptive transformations are equivalent to standard Hermite approximation of the pullback function, yielding error bounds controlled by the regularity of that pullback and enabling spectral convergence via a monotone transport map that aligns decay.
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A new error decomposition framework for scaled Hermite spectral methods shows that balancing spatial and frequency truncation errors via scaling recovers geometric convergence and doubles algebraic convergence orders.
Optimal asymptotic estimates for Laguerre and Hermite coefficient decay for functions with algebraic and logarithmic singularities, yielding convergence rates for spectral orthogonal projections.
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Convergence theory for Hermite approximations under adaptive coordinate transformations
Hermite approximations composed with adaptive transformations are equivalent to standard Hermite approximation of the pullback function, yielding error bounds controlled by the regularity of that pullback and enabling spectral convergence via a monotone transport map that aligns decay.
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Scaling Optimized Hermite Approximation Methods
A new error decomposition framework for scaled Hermite spectral methods shows that balancing spatial and frequency truncation errors via scaling recovers geometric convergence and doubles algebraic convergence orders.
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Optimal asymptotic analyses on Laguerre and Hermite orthogonal approximation for functions of algebraic and logarithmic regularitiesYali
Optimal asymptotic estimates for Laguerre and Hermite coefficient decay for functions with algebraic and logarithmic singularities, yielding convergence rates for spectral orthogonal projections.