2013/07/30 by Javier Garcia, Javier G. García, Francisco M Fernández +3
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Analysis Techniques #Algorithm #Applied mathematics #Basis (linear algebra) #Computer science #Convergence (economics) #FOS: Physical sciences #Geometry #Image and Signal Denoising Methods #Mathematical Physics (math-ph) #Mathematical analysis #Mathematics #Model Reduction and Neural Networks #Orthogonal polynomials #Orthographic projection #Polynomial #Projection (relational algebra) #Quantization (signal processing) #Rate of convergence #Rayleigh–Ritz method #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1308.0001
published in arXiv (Cornell University) (Cornell University)
arxiv created 2013/07/30 · openalex publication_date 2013/07/30 · arxiv updated 2013/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We discuss Rayleigh-Ritz variational calculations with nonorthogonal basis sets that exhibit the correct asymptotic behaviour. We construct the suitable basis sets for general one-dimensional models and illustrate the application of the approach on two double-well oscillators proposed recently by other authors. The rate of convergence of the variational method proves to be considerably greater than the one exhibited by the recently developed orthogonal polynomial projection quantization.