Discrete Spherical Harmonic Transforms: Numerical Preconditioning and Optimization

Discrete Spherical Harmonic Transforms for Equiangular Grids of Spatial and Spectral Data

Spherical Harmonic Transforms (SHTs) which are non-commutative Fourier transforms on the sphere are critical in global geopotential and related applications. Among the best known global strategies for discrete SHTs of band-limited spherical functions are Chebychev quadratures and least squares for equiangular grids. With proper numerical preconditioning, independent of latitude, reliable analys...

Optimization of Spherical Harmonic Transform Computations

Spherical Harmonic Transforms (SHTs) which are essentially Fourier transforms on the sphere are critical in global geopotential and related applications. Discrete SHTs are more complex to optimize computationally than Fourier transforms in the sense of the well-known Fast Fourier Transforms (FFTs). Furthermore, for analysis purposes, discrete SHTs are difficult to formulate for an optimal discr...

Numerical Solution of Volterra-Fredholm Integral Equations with The Help of Inverse and Direct Discrete Fuzzy Transforms and Collocation Technique

Fast, exact (but unstable) spin spherical harmonic transforms

We derive algorithms to perform a spin spherical harmonic transform and inverse for functions of arbitrary spin number. These algorithms involve recasting the spin transform on the two-sphere S as a Fourier transform on the two-torus T. Fast Fourier transforms are then used to compute Fourier coefficients, which are related to spherical harmonic coefficients through a linear transform. By recas...

Spherical Harmonic Transforms Using Quadratures and Least Squares

Spherical Harmonic Transforms (SHTs) which are essentially Fourier transforms on the sphere are critical in global geopotential and related applications. For analysis purposes, discrete SHTs are difficult to formulate for an optimal discretization of the sphere, especially for applications with requirements in terms of near-isometric grids and special considerations in the polar regions. With t...