This repository contains MATLAB livescripts and files corresponding to the paper “Solution of Ill-posed Problems with Chebfun” by Abdulaziz Alqahtani, Thomas Mach, Lothar Reichel, Numerical Algorithms, TBA.
The code was tested with MATLAB R2020b and the latest release of Chebfun (v.5.7.0). The Chebfun package is available on github under https://github.com/chebfun/chebfun.
The examples are mostly modified version of Regularization Tools Version 4.1. One example is inspired by
Gazzola, S., Hansen, P. C., & Nagy, J. G. (2019). IR Tools: a MATLAB package of iterative regularization methods and large-scale test problems. Numerical Algorithms, 81(3), 773-811.
Copyright (c) 2022 Abdulaziz Alqahtani, Thomas Mach, Lothar Reichel
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
Some files are modified files originally published by Per Christian Hansen (DTU) under a 3-Clause BSD License. The license for these files is stated at the begin of the relevant files.
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Abdulaziz Alqahtani King Khalid University — Saudi Aradbia Kent State University — USA e-mail: [email protected]
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Thomas Mach University of Potsdam — Germany e-mail: [email protected]
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Lothar Reichel Kent State University — USA e-mail: [email protected]
- Solution of Ill-Posed Problems with Chebfun NUMERICAL ALGORITHMS, TBA. Package na54
- V1.0, July 2022
- Matlab
- Chebfun 5.7.0 or newer (available from https://github.com/chebfun/chebfun)
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README.txt
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LICENSE license file
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baart.m, fox_goodwin.m, gravity.m, shaw.m, wing.m definition of examples from Regularization Tools by Per Christian Hansen the files have been modified to provide the used discretization
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baart_chebfun.m, fox_goodwin_chebfun.m gravity_chebfun.m, shaw_chebfun.m wing_chebfun.m continuous version of the examples above using Chebfun
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Solution_of_Ill_posed_Problems_with_Chebfun_1d/2d_live.mlx Matlab livescripts demonstrating how the examples can be solved
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svd4.m singular value decomposition for four dimensional functions using adaptive cross approximation
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errlambda1/2b/3.m, twod_errlambda1.m support function different version of objective functions for the different examples
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relative_error_norm.m/relative_error_norm_sqrt.m support function
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weighted_euclidean_norm.m support function