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Variable transformation and scaling are performed to avoid underflows and overflows during the calculations. A special linear solver using the eigenvalues and eigenvectors of the Jacobian matrix is implemented for overcoming disastrous singularity of this matrix, and the singular value decomposition method is applied for setting the initial guess. In addition, polynomial extrapolation is used for improving the performance when simulating a diagram of concentrations of species. The method was tested with 14 systems of different sizes over the whole pH range and presented robust and efficient behavior. \u00a9 1995 by John Wiley &amp; Sons, Inc.<\/jats:p>","DOI":"10.1002\/jcc.540160503","type":"journal-article","created":{"date-parts":[[2005,1,2]],"date-time":"2005-01-02T01:09:09Z","timestamp":1104628149000},"page":"534-544","source":"Crossref","is-referenced-by-count":2,"title":["The exponents method for calculating equilibrium concentrations of complex species in solution"],"prefix":"10.1002","volume":"16","author":[{"given":"Frederico F.","family":"Campos","sequence":"first","affiliation":[]},{"given":"John S.","family":"Rollett","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2004,9,7]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0039-9140(77)80046-5"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0039-9140(75)80171-8"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0039-9140(67)80105-X"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/0039-9140(76)80039-2"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1021\/ac60320a007"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/0039-9140(74)80063-9"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-1693(00)95610-X"},{"key":"e_1_2_1_9_2","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/0097-8485(84)80005-4","volume":"8","author":"Garcia A.","year":"1984","journal-title":"Comp. 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