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As another major contribution, efficient numerical implementation based on matrix exponential in time is developed, which shows much improved computational efficiency than MATLAB's backslash solver based on the all-at-once space-time discretization scheme. Numerical examples are reported to illustrate the promising computational performance of our proposed algorithms based on matrix exponential techniques.&lt;\/p&gt;&lt;\/abstract&gt;<\/jats:p>","DOI":"10.3934\/nhm.2023026","type":"journal-article","created":{"date-parts":[[2023,2,7]],"date-time":"2023-02-07T09:38:38Z","timestamp":1675762718000},"page":"601-621","source":"Crossref","is-referenced-by-count":3,"title":["Fast matrix exponential-based quasi-boundary value methods for inverse space-dependent source problems"],"prefix":"10.3934","volume":"18","author":[{"given":"Ferm\u00edn S. 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