@misc{garde_linearised_2024,
	title = {Linearised {Calder}{\textbackslash}'on problem: {Reconstruction} of unbounded perturbations in {3D}},
	shorttitle = {Linearised {Calder}{\textbackslash}'on problem},
	url = {http://arxiv.org/abs/2403.16588},
	doi = {10.48550/arXiv.2403.16588},
	abstract = {Recently an algorithm was given in [Garde \& Hyv{\textbackslash}"onen, SIAM J. Math. Anal., 2024] for exact direct reconstruction of any \$L{\textasciicircum}2\$ perturbation from linearised data in the two-dimensional linearised Calder{\textbackslash}'on problem. It was a simple forward substitution method based on a 2D Zernike basis. We now consider the three-dimensional linearised Calder{\textbackslash}'on problem in a ball, and use a 3D Zernike basis to obtain a method for exact direct reconstruction of any \$L{\textasciicircum}3\$ perturbation from linearised data. The method is likewise a forward substitution, hence making it very efficient to numerically implement. Moreover, the 3D method only makes use of a relatively small subset of boundary measurements for exact reconstruction, compared to a full \$L{\textasciicircum}2\$ basis of current densities.},
	urldate = {2024-06-27},
	publisher = {arXiv},
	author = {Garde, Henrik and Hirvensalo, Markus},
	month = mar,
	year = {2024},
	note = {arXiv:2403.16588 [cs, math]
version: 1},
	keywords = {Calderón problem, inverse problems, mentions sympy, numerical analysis, partial differential equations},
}

{"_id":"baF5CdzHysHujegsm","bibbaseid":"garde-hirvensalo-linearisedcalderonproblemreconstructionofunboundedperturbationsin3d-2024","author_short":["Garde, H.","Hirvensalo, M."],"bibdata":{"bibtype":"misc","type":"misc","title":"Linearised Calder\\'on problem: Reconstruction of unbounded perturbations in 3D","shorttitle":"Linearised Calder\\'on problem","url":"http://arxiv.org/abs/2403.16588","doi":"10.48550/arXiv.2403.16588","abstract":"Recently an algorithm was given in [Garde & Hyv\\\"onen, SIAM J. Math. Anal., 2024] for exact direct reconstruction of any $L{\\textasciicircum}2$ perturbation from linearised data in the two-dimensional linearised Calder\\'on problem. It was a simple forward substitution method based on a 2D Zernike basis. We now consider the three-dimensional linearised Calder\\'on problem in a ball, and use a 3D Zernike basis to obtain a method for exact direct reconstruction of any $L{\\textasciicircum}3$ perturbation from linearised data. The method is likewise a forward substitution, hence making it very efficient to numerically implement. Moreover, the 3D method only makes use of a relatively small subset of boundary measurements for exact reconstruction, compared to a full $L{\\textasciicircum}2$ basis of current densities.","urldate":"2024-06-27","publisher":"arXiv","author":[{"propositions":[],"lastnames":["Garde"],"firstnames":["Henrik"],"suffixes":[]},{"propositions":[],"lastnames":["Hirvensalo"],"firstnames":["Markus"],"suffixes":[]}],"month":"March","year":"2024","note":"arXiv:2403.16588 [cs, math] version: 1","keywords":"Calderón problem, inverse problems, mentions sympy, numerical analysis, partial differential equations","bibtex":"@misc{garde_linearised_2024,\n\ttitle = {Linearised {Calder}{\\textbackslash}'on problem: {Reconstruction} of unbounded perturbations in {3D}},\n\tshorttitle = {Linearised {Calder}{\\textbackslash}'on problem},\n\turl = {http://arxiv.org/abs/2403.16588},\n\tdoi = {10.48550/arXiv.2403.16588},\n\tabstract = {Recently an algorithm was given in [Garde \\& Hyv{\\textbackslash}\"onen, SIAM J. Math. Anal., 2024] for exact direct reconstruction of any \\$L{\\textasciicircum}2\\$ perturbation from linearised data in the two-dimensional linearised Calder{\\textbackslash}'on problem. It was a simple forward substitution method based on a 2D Zernike basis. We now consider the three-dimensional linearised Calder{\\textbackslash}'on problem in a ball, and use a 3D Zernike basis to obtain a method for exact direct reconstruction of any \\$L{\\textasciicircum}3\\$ perturbation from linearised data. The method is likewise a forward substitution, hence making it very efficient to numerically implement. Moreover, the 3D method only makes use of a relatively small subset of boundary measurements for exact reconstruction, compared to a full \\$L{\\textasciicircum}2\\$ basis of current densities.},\n\turldate = {2024-06-27},\n\tpublisher = {arXiv},\n\tauthor = {Garde, Henrik and Hirvensalo, Markus},\n\tmonth = mar,\n\tyear = {2024},\n\tnote = {arXiv:2403.16588 [cs, math]\nversion: 1},\n\tkeywords = {Calderón problem, inverse problems, mentions sympy, numerical analysis, partial differential equations},\n}\n\n\n\n\n\n\n\n\n\n\n\n","author_short":["Garde, H.","Hirvensalo, M."],"key":"garde_linearised_2024","id":"garde_linearised_2024","bibbaseid":"garde-hirvensalo-linearisedcalderonproblemreconstructionofunboundedperturbationsin3d-2024","role":"author","urls":{"Paper":"http://arxiv.org/abs/2403.16588"},"keyword":["Calderón problem","inverse problems","mentions sympy","numerical analysis","partial differential equations"],"metadata":{"authorlinks":{}}},"bibtype":"misc","biburl":"https://bibbase.org/zotero-group/nicoguaro/525293","dataSources":["YtBDXPDiQEyhyEDZC","Kty8eEAcNZykiCCnc"],"keywords":["calderón problem","inverse problems","mentions sympy","numerical analysis","partial differential equations"],"search_terms":["linearised","calder","problem","reconstruction","unbounded","perturbations","garde","hirvensalo"],"title":"Linearised Calder\\'on problem: Reconstruction of unbounded perturbations in 3D","year":2024}