@Book{Allgower2003a,
    author      = {Allgower, E. and Georg, K.},
    title       = {Introduction to {Numerical} {Continuation} {Methods}},
    doi         = {10.1137/1.9780898719154},
    isbn        = {978-0-89871-544-6},
    month       = {January},
    publisher   = {Society for Industrial and Applied Mathematics},
    series      = {Classics in {Applied} {Mathematics}},
    year        = {2003},
    abstract    = {This book was intended as an introduction to the topic of numerical continuation which would be accessible to a readership of widely varying mathematical backgrounds. Realizing the close relationship which exists between the predictor-corrector and the piecewise linear continuation approaches, we attempted to present both methods in a unified way. In the belief that potential users of numerical continuation methods would create programs adapted to their particular needs, we presented pseudo codes and Fortran codes merely as illustrations. Indeed, there are now many specialized packages for treating such varied problems as bifurcation, polynomial systems, eigenvalues, economic equilibria, optimization, and the approximation of manifolds. It was gratifying to hear from students and young colleagues that they had learned from the book in seminars and had used it as a guidebook to write codes tailored to their needs. We hope that this edition can continue to serve such a
                  purpose. Although the original book contained a comprehensive bibliography for its time, a great deal of new literature and software has since appeared. Indeed, for this preface we must content ourselves with an updating of the literature by giving a partial listing of books, survey articles, and conference proceedings dealing with numerical continuation methods and their applications. These sources themselves contain many additional references. Similarly, concerning software, we present several URLs from which readers can hopefully proceed to look for codes which may meet their needs. Remarkably, essentially all of the books treating numerical continuation and/or bifurcation listed in the original bibliography are presently out of print, e.g., Garcia and Zangwill [14], H. B. Keller [20], Rheinboldt [31], and Todd [37]. Only the book by Seydel [35] treating bifurcation and stability analysis is still available. Govaerts has recently authored a monograph [16] on
                  numerical bifurcation of dynamical systems. This book has an extensive bibliography. A somewhat more numerically oriented book has been written by Kuznetsov [22]. Among the conference proceedings treating various aspects of numerical continuation including bifurcation, homotopy methods, and exploiting symmetry are [1, 2, 6, 19, 26, 30, 36]. Homotopy continuation methods for solving polynomial systems over complex numbers has been a very active topic. This is surveyed in the papers by Li [24, 25].}
}

{"_id":{"_str":"521a81b6aa2f288d1f0008cd"},"__v":0,"authorIDs":[],"author_short":["Allgower, E.","Georg, K."],"bibbaseid":"allgower-georg-introductiontonumericalcontinuationmethods-2003","bibdata":{"bibtype":"book","type":"book","author":[{"propositions":[],"lastnames":["Allgower"],"firstnames":["E."],"suffixes":[]},{"propositions":[],"lastnames":["Georg"],"firstnames":["K."],"suffixes":[]}],"title":"Introduction to Numerical Continuation Methods","doi":"10.1137/1.9780898719154","isbn":"978-0-89871-544-6","month":"January","publisher":"Society for Industrial and Applied Mathematics","series":"Classics in Applied Mathematics","year":"2003","abstract":"This book was intended as an introduction to the topic of numerical continuation which would be accessible to a readership of widely varying mathematical backgrounds. Realizing the close relationship which exists between the predictor-corrector and the piecewise linear continuation approaches, we attempted to present both methods in a unified way. In the belief that potential users of numerical continuation methods would create programs adapted to their particular needs, we presented pseudo codes and Fortran codes merely as illustrations. Indeed, there are now many specialized packages for treating such varied problems as bifurcation, polynomial systems, eigenvalues, economic equilibria, optimization, and the approximation of manifolds. It was gratifying to hear from students and young colleagues that they had learned from the book in seminars and had used it as a guidebook to write codes tailored to their needs. We hope that this edition can continue to serve such a purpose. Although the original book contained a comprehensive bibliography for its time, a great deal of new literature and software has since appeared. Indeed, for this preface we must content ourselves with an updating of the literature by giving a partial listing of books, survey articles, and conference proceedings dealing with numerical continuation methods and their applications. These sources themselves contain many additional references. Similarly, concerning software, we present several URLs from which readers can hopefully proceed to look for codes which may meet their needs. Remarkably, essentially all of the books treating numerical continuation and/or bifurcation listed in the original bibliography are presently out of print, e.g., Garcia and Zangwill [14], H. B. Keller [20], Rheinboldt [31], and Todd [37]. Only the book by Seydel [35] treating bifurcation and stability analysis is still available. Govaerts has recently authored a monograph [16] on numerical bifurcation of dynamical systems. This book has an extensive bibliography. A somewhat more numerically oriented book has been written by Kuznetsov [22]. Among the conference proceedings treating various aspects of numerical continuation including bifurcation, homotopy methods, and exploiting symmetry are [1, 2, 6, 19, 26, 30, 36]. Homotopy continuation methods for solving polynomial systems over complex numbers has been a very active topic. This is surveyed in the papers by Li [24, 25].","bibtex":"@Book{Allgower2003a,\n author = {Allgower, E. and Georg, K.},\n title = {Introduction to {Numerical} {Continuation} {Methods}},\n doi = {10.1137/1.9780898719154},\n isbn = {978-0-89871-544-6},\n month = {January},\n publisher = {Society for Industrial and Applied Mathematics},\n series = {Classics in {Applied} {Mathematics}},\n year = {2003},\n abstract = {This book was intended as an introduction to the topic of numerical continuation which would be accessible to a readership of widely varying mathematical backgrounds. Realizing the close relationship which exists between the predictor-corrector and the piecewise linear continuation approaches, we attempted to present both methods in a unified way. In the belief that potential users of numerical continuation methods would create programs adapted to their particular needs, we presented pseudo codes and Fortran codes merely as illustrations. Indeed, there are now many specialized packages for treating such varied problems as bifurcation, polynomial systems, eigenvalues, economic equilibria, optimization, and the approximation of manifolds. It was gratifying to hear from students and young colleagues that they had learned from the book in seminars and had used it as a guidebook to write codes tailored to their needs. We hope that this edition can continue to serve such a\n purpose. Although the original book contained a comprehensive bibliography for its time, a great deal of new literature and software has since appeared. Indeed, for this preface we must content ourselves with an updating of the literature by giving a partial listing of books, survey articles, and conference proceedings dealing with numerical continuation methods and their applications. These sources themselves contain many additional references. Similarly, concerning software, we present several URLs from which readers can hopefully proceed to look for codes which may meet their needs. Remarkably, essentially all of the books treating numerical continuation and/or bifurcation listed in the original bibliography are presently out of print, e.g., Garcia and Zangwill [14], H. B. Keller [20], Rheinboldt [31], and Todd [37]. Only the book by Seydel [35] treating bifurcation and stability analysis is still available. Govaerts has recently authored a monograph [16] on\n numerical bifurcation of dynamical systems. This book has an extensive bibliography. A somewhat more numerically oriented book has been written by Kuznetsov [22]. Among the conference proceedings treating various aspects of numerical continuation including bifurcation, homotopy methods, and exploiting symmetry are [1, 2, 6, 19, 26, 30, 36]. Homotopy continuation methods for solving polynomial systems over complex numbers has been a very active topic. 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