Academic Journal
Randomized Least-Squares with Minimal Oversampling and Interpolation in General Spaces
| Τίτλος: | Randomized Least-Squares with Minimal Oversampling and Interpolation in General Spaces |
|---|---|
| Συγγραφείς: | Matthieu Dolbeault, Moulay Abdellah Chkifa |
| Πηγή: | SIAM Journal on Numerical Analysis. 62:1515-1538 |
| Publication Status: | Preprint |
| Στοιχεία εκδότη: | Society for Industrial & Applied Mathematics (SIAM), 2024. |
| Έτος έκδοσης: | 2024 |
| Θεματικοί όροι: | Convex Optimization, Computational Mechanics, Polynomial, Mathematical analysis, Estimator, Bandwidth (computing), Filter (signal processing), Sparse Approximation, Engineering, High-dimensional Integration and Quasi-Monte Carlo Methods, Machine learning, FOS: Mathematics, Mathematics - Numerical Analysis, Multivariate Approximation, Stability (learning theory), Numerical Analysis, Computer network, Randomized Methods, Computer graphics (images), Oversampling, Mathematical optimization, Statistics, Numerical Analysis (math.NA), Sampling (signal processing), Animation, 65D15, 41A65, 65D05, 41A81, 41A05, Theory and Applications of Compressed Sensing, Applied mathematics, Computer science, Discrepancy Minimization, Dimension (graph theory), Combinatorics, Physical Sciences, Computer Science, Interpolation (computer graphics), Computer vision, Computer Vision and Pattern Recognition, Image Denoising Techniques and Algorithms, Mathematics, Least-squares function approximation |
| Περιγραφή: | In approximation of functions based on point values, least-squares methods provide more stability than interpolation, at the expense of increasing the sampling budget. We show that near-optimal approximation error can nevertheless be achieved, in an expected $L^2$ sense, as soon as the sample size $m$ is larger than the dimension $n$ of the approximation space by a constant ratio. On the other hand, for $m=n$, we obtain an interpolation strategy with a stability factor of order $n$. The proposed sampling algorithms are greedy procedures based on arXiv:0808.0163 and arXiv:1508.03261, with polynomial computational complexity. 17 pages |
| Τύπος εγγράφου: | Article Other literature type |
| Γλώσσα: | English |
| ISSN: | 1095-7170 0036-1429 |
| DOI: | 10.1137/23m160178x |
| DOI: | 10.48550/arxiv.2306.07435 |
| DOI: | 10.60692/ehsg8-k5172 |
| DOI: | 10.60692/83c9v-8dd14 |
| Σύνδεσμος πρόσβασης: | http://arxiv.org/abs/2306.07435 |
| Rights: | CC BY |
| Αριθμός Καταχώρησης: | edsair.doi.dedup.....04cc447764ea5c09bd416c7a8e40285b |
| Βάση Δεδομένων: | OpenAIRE |
| ISSN: | 10957170 00361429 |
|---|---|
| DOI: | 10.1137/23m160178x |