Edit Profile (opens in new tab) Schönhage, Arnold Co-Author Distance Author ID: schonhage.arnold Published as: Schönhage, A.; Schönhage, Arnold; Schoenhage, Arnold; Schoenhage, A. more...less External Links: MGP · Wikidata · dblp · GND Documents Indexed: 60 Publications since 1957, including 2 Books Co-Authors: 10 Co-Authors with 9 Joint Publications 616 Co-Co-Authors all top 5 Co-Authors 51 single-authored 2 Saff, Edward Barry 2 Strassen, Volker 2 Varga, Richard Steven 1 Grotefeld, Andreas 1 Knuth, Donald Ervin 1 Lorenz, Falko 1 Odlyzko, Andrew M. 1 Paterson, Mike S. 1 Pippenger, Nicholas J. 1 Vetter, Ekkehart all top 5 Serials 8 Numerische Mathematik 3 Archiv der Mathematik 3 Mathematische Zeitschrift 3 Theoretical Computer Science 2 Acta Informatica 2 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 2 Computing 2 Journal of Approximation Theory 2 Kiberneticheskiĭ Sbornik. Novaya Seriya 2 SIAM Journal on Computing 1 Information Processing Letters 1 Blätter (Deutsche Gesellschaft für Versicherungsmathematik) 1 Journal of the Association for Computing Machinery 1 Journal of Computer and System Sciences 1 Mathematische Annalen 1 SIAM Journal on Numerical Analysis 1 Transactions of the American Mathematical Society 1 Journal of Algorithms 1 Journal of Symbolic Computation 1 Journal of Complexity 1 Bulletin of the European Association for Theoretical Computer Science (EATCS) 1 Linear Algebra and its Applications 1 Mathematisch-Physikalische Semesterberichte, Neue Folge all top 5 Fields 30 Computer science (68-XX) 17 Numerical analysis (65-XX) 7 Field theory and polynomials (12-XX) 7 Approximations and expansions (41-XX) 6 Number theory (11-XX) 3 Mathematical logic and foundations (03-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Real functions (26-XX) 1 Special functions (33-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Statistics (62-XX) 1 Operations research, mathematical programming (90-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 47 Publications have been cited 1,027 times in 886 Documents Cited by ▼ Year ▼ Fast multiplication of large numbers. (Schnelle Multiplikation großer Zahlen.) Zbl 0223.68007 Schönhage, A.; Strassen, V. 302 1971 Partial and total matrix multiplication. Zbl 0462.68018 Schönhage, A. 67 1981 Fast multiplication of polynomials over fields of characteristic 2. (Schnelle Multiplikation von Polynomen über Körpern der Charakteristik 2.) Zbl 0362.65011 Schönhage, A. 54 1977 Fast computation of continued fraction expansions. (Schnelle Berechnung von Kettenbruchentwicklungen.) Zbl 0223.68008 Schönhage, A. 49 1971 Finding the median. Zbl 0335.68033 Schoenhage, A.; Paterson, M.; Pippenger, N. 46 1976 Storage modification machines. Zbl 0454.68034 Schönhage, A. 44 1980 Quasi-gcd computations. Zbl 0586.68031 Schönhage, Arnold 41 1985 Fast algorithms for multiple evaluations of the Riemann zeta function. Zbl 0706.11047 Odlyzko, A. M.; Schönhage, A. 35 1988 Fehlerfortpflanzung bei Interpolation. Zbl 0125.07501 Schönhage, A. 34 1961 Approximationstheorie. Zbl 0212.41501 Schönhage, A. 31 1971 The expected linearity of a simple equivalence algorithm. Zbl 0377.68024 Knuth, Donald E.; Schönhage, Arnold 31 1978 Asymptotically fast algorithms for the numerical multiplication and division of polynomials with complex coefficients. Zbl 0538.68035 Schönhage, Arnold 23 1982 Zur rationalen Approximierbarkeit von \(e^{-x}\) über \([0, \infty)\). Zbl 0279.41011 Schönhage, A. 22 1973 Fast algorithms. A multitape Turing machine implementation. Zbl 0853.68108 Schönhage, Arnold; Grotefeld, Andreas; Vetter, Ekkehart 22 1994 Zur Konvergenz des Jacobi-Verfahrens. Zbl 0100.33105 Schönhage, A. 17 1961 On the power of random access machines. Zbl 0409.68030 Schönhage, Arnold 17 1979 Geometric convergence to \(e^{-z}\) by rational functions with real poles. Zbl 0307.65025 Saff, E. B.; Schönhage, A.; Varga, R. S. 15 1976 Fast reduction and composition of binary quadratic forms. Zbl 1019.11505 Schönhage, Arnold 14 1991 Über das Wachstum zusammengesetzter Funktionen. Zbl 0123.26703 Schönhage, Arnold 14 1960 Eine Bemerkung zur Konstruktion großer Primzahllücken. Zbl 0108.04504 Schönhage, Arnold 13 1963 A lower bound for the length of addition chains. Zbl 0307.68032 Schönhage, Arnold 13 1975 Polynomial root separation examples. Zbl 1158.12300 Schönhage, Arnold 12 2006 Zur quadratischen Konvergenz des Jacobi-Verfahrens.(On quadrative convergence of the Jacobi method). Zbl 0221.65066 Schönhage, A. 12 1964 Numerics of analytic functions and complexity. (Numerik analytischer Funktionen und Komplexität.) Zbl 0797.68090 Schönhage, A. 11 1990 Factorization of univariate integer polynomials by diophantine approximation and an improved basis reduction algorithm. Zbl 0569.68030 Schönhage, Arnold 11 1984 Unitäre Transformationen großer Matrizen. Zbl 0252.65031 Schönhage, A. 8 1973 Optimale Punkte für Differentiation und Integration. Zbl 0196.48902 Schönhage, A. 8 1963 Variations on computing reciprocals of power series. Zbl 1014.68065 Schönhage, Arnold 8 2000 Lebesguekonstanten bei numerischer Differentiation. Zbl 0141.33501 Schönhage, A. 6 1966 Schnelle Multiplikation großer Zahlen. Zbl 0271.68051 Schönhage, A.; Strassen, V. 5 1973 Zur Quadratur holomorpher periodischer Funktionen. Zbl 0327.65021 Schönhage, Arnold 5 1975 Multiplikation großer Zahlen. Zbl 0196.52104 Schönhage, A. 5 1966 Mehrdimensionale Romberg-Integration. Zbl 0182.49503 Schönhage, Arnold 4 1970 The production of partial orders. Zbl 0383.68053 Schönhage, A. 4 1976 Probabilistic computation of integer polynomial GCDs. Zbl 0651.68045 Schönhage, A. 3 1988 A nonlinear lower bound for random-access machines under logarithmic cost. Zbl 0661.68040 Schönhage, Arnold 3 1988 Fast parallel computation of characteristic polynomials by Leverrier’s power sum method adapted to fields of finite characteristic. Zbl 1422.68330 Schönhage, Arnold 3 1993 Über ein zahlentheoretisches Problem aus der Fourieranalysis. (On a number-theoretic problem from Fourier analysis). Zbl 0212.09501 Lorenz, F.; Schönhage, A. 2 1971 Zum Schubfaecherprinzip im linearen Intervall. Zbl 0079.07303 Schönhage, Arnold 2 1957 Zur Konvergenz der Stufenpolynome über den Nullstellen der Legendre- Polynome. Zbl 0269.41003 Schönhage, A. 2 1972 Fast Schmidt orthogonalization and unitary transformations of large matrices. Zbl 0286.68030 Schönhage, Arnold 2 1973 Von den ganzen zu den reellen Zahlen. Zbl 0196.07402 Schönhage, A. 2 1970 Rational approximation to \(e^{-x}\) and related \(L^ 2\)-problems. Zbl 0514.41018 Schoenhage, Arnold 1 1982 Universelle Turing Speicherung. Zbl 0215.32201 Schönhage, A. 1 1970 Bivariate polynomial multiplication patterns. Zbl 0911.12007 Schönhage, Arnold 1 1995 An elementary proof for Strassen’s degree bound. Zbl 0363.65012 Schönhage, Arnold 1 1977 Tapes versus pointers: A study in implementing fast algorithms. Zbl 1023.68582 Schönhage, Arnold 1 1986 Polynomial root separation examples. Zbl 1158.12300 Schönhage, Arnold 12 2006 Variations on computing reciprocals of power series. Zbl 1014.68065 Schönhage, Arnold 8 2000 Bivariate polynomial multiplication patterns. Zbl 0911.12007 Schönhage, Arnold 1 1995 Fast algorithms. A multitape Turing machine implementation. Zbl 0853.68108 Schönhage, Arnold; Grotefeld, Andreas; Vetter, Ekkehart 22 1994 Fast parallel computation of characteristic polynomials by Leverrier’s power sum method adapted to fields of finite characteristic. Zbl 1422.68330 Schönhage, Arnold 3 1993 Fast reduction and composition of binary quadratic forms. Zbl 1019.11505 Schönhage, Arnold 14 1991 Numerics of analytic functions and complexity. (Numerik analytischer Funktionen und Komplexität.) Zbl 0797.68090 Schönhage, A. 11 1990 Fast algorithms for multiple evaluations of the Riemann zeta function. Zbl 0706.11047 Odlyzko, A. M.; Schönhage, A. 35 1988 Probabilistic computation of integer polynomial GCDs. Zbl 0651.68045 Schönhage, A. 3 1988 A nonlinear lower bound for random-access machines under logarithmic cost. Zbl 0661.68040 Schönhage, Arnold 3 1988 Tapes versus pointers: A study in implementing fast algorithms. Zbl 1023.68582 Schönhage, Arnold 1 1986 Quasi-gcd computations. Zbl 0586.68031 Schönhage, Arnold 41 1985 Factorization of univariate integer polynomials by diophantine approximation and an improved basis reduction algorithm. Zbl 0569.68030 Schönhage, Arnold 11 1984 Asymptotically fast algorithms for the numerical multiplication and division of polynomials with complex coefficients. Zbl 0538.68035 Schönhage, Arnold 23 1982 Rational approximation to \(e^{-x}\) and related \(L^ 2\)-problems. Zbl 0514.41018 Schoenhage, Arnold 1 1982 Partial and total matrix multiplication. Zbl 0462.68018 Schönhage, A. 67 1981 Storage modification machines. Zbl 0454.68034 Schönhage, A. 44 1980 On the power of random access machines. Zbl 0409.68030 Schönhage, Arnold 17 1979 The expected linearity of a simple equivalence algorithm. Zbl 0377.68024 Knuth, Donald E.; Schönhage, Arnold 31 1978 Fast multiplication of polynomials over fields of characteristic 2. (Schnelle Multiplikation von Polynomen über Körpern der Charakteristik 2.) Zbl 0362.65011 Schönhage, A. 54 1977 An elementary proof for Strassen’s degree bound. Zbl 0363.65012 Schönhage, Arnold 1 1977 Finding the median. Zbl 0335.68033 Schoenhage, A.; Paterson, M.; Pippenger, N. 46 1976 Geometric convergence to \(e^{-z}\) by rational functions with real poles. Zbl 0307.65025 Saff, E. B.; Schönhage, A.; Varga, R. S. 15 1976 The production of partial orders. Zbl 0383.68053 Schönhage, A. 4 1976 A lower bound for the length of addition chains. Zbl 0307.68032 Schönhage, Arnold 13 1975 Zur Quadratur holomorpher periodischer Funktionen. Zbl 0327.65021 Schönhage, Arnold 5 1975 Zur rationalen Approximierbarkeit von \(e^{-x}\) über \([0, \infty)\). Zbl 0279.41011 Schönhage, A. 22 1973 Unitäre Transformationen großer Matrizen. Zbl 0252.65031 Schönhage, A. 8 1973 Schnelle Multiplikation großer Zahlen. Zbl 0271.68051 Schönhage, A.; Strassen, V. 5 1973 Fast Schmidt orthogonalization and unitary transformations of large matrices. Zbl 0286.68030 Schönhage, Arnold 2 1973 Zur Konvergenz der Stufenpolynome über den Nullstellen der Legendre- Polynome. Zbl 0269.41003 Schönhage, A. 2 1972 Fast multiplication of large numbers. (Schnelle Multiplikation großer Zahlen.) Zbl 0223.68007 Schönhage, A.; Strassen, V. 302 1971 Fast computation of continued fraction expansions. (Schnelle Berechnung von Kettenbruchentwicklungen.) Zbl 0223.68008 Schönhage, A. 49 1971 Approximationstheorie. Zbl 0212.41501 Schönhage, A. 31 1971 Über ein zahlentheoretisches Problem aus der Fourieranalysis. (On a number-theoretic problem from Fourier analysis). Zbl 0212.09501 Lorenz, F.; Schönhage, A. 2 1971 Mehrdimensionale Romberg-Integration. Zbl 0182.49503 Schönhage, Arnold 4 1970 Von den ganzen zu den reellen Zahlen. Zbl 0196.07402 Schönhage, A. 2 1970 Universelle Turing Speicherung. Zbl 0215.32201 Schönhage, A. 1 1970 Lebesguekonstanten bei numerischer Differentiation. Zbl 0141.33501 Schönhage, A. 6 1966 Multiplikation großer Zahlen. Zbl 0196.52104 Schönhage, A. 5 1966 Zur quadratischen Konvergenz des Jacobi-Verfahrens.(On quadrative convergence of the Jacobi method). Zbl 0221.65066 Schönhage, A. 12 1964 Eine Bemerkung zur Konstruktion großer Primzahllücken. Zbl 0108.04504 Schönhage, Arnold 13 1963 Optimale Punkte für Differentiation und Integration. Zbl 0196.48902 Schönhage, A. 8 1963 Fehlerfortpflanzung bei Interpolation. Zbl 0125.07501 Schönhage, A. 34 1961 Zur Konvergenz des Jacobi-Verfahrens. Zbl 0100.33105 Schönhage, A. 17 1961 Über das Wachstum zusammengesetzter Funktionen. Zbl 0123.26703 Schönhage, Arnold 14 1960 Zum Schubfaecherprinzip im linearen Intervall. Zbl 0079.07303 Schönhage, Arnold 2 1957 all cited Publications top 5 cited Publications all top 5 Cited by 1,116 Authors 23 Pan, Victor Yakovlevich 21 van der Hoeven, Joris 18 Schost, Éric 15 Harvey, David 14 von zur Gathen, Joachim 9 Bini, Dario Andrea 9 Bostan, Alin 9 Forst, Wilhelm 9 Lecerf, Grégoire 9 Schönhage, Arnold 9 Sutherland, Andrew V. 8 Flajolet, Philippe 8 Hiary, Ghaith Ayesh 8 Landsberg, Joseph Montague 8 Lickteig, Thomas 7 Jeannerod, Claude-Pierre 7 Pittel, Boris G. 7 Salvy, Bruno 7 Sergeev, Igor’ Sergeevich 7 Villard, Gilles 6 Karatsuba, Ekaterina Anatol’evna 6 Moreno Maza, Marc 6 Reddy, A. R. 5 Büthe, Jan 5 Christandl, Matthias 5 Crandall, Richard E. 5 Devroye, Luc P. J. A. 5 Dubickas, Artūras 5 Dumitrescu, Adrian 5 Gashkov, Sergey B. 5 Giesbrecht, Mark W. 5 Kaltofen, Erich L. 5 Lingas, Andrzej 5 Sagraloff, Michael 5 Storjohann, Arne 5 Takahashi, Daisuke A. 4 Alman, Josh 4 Baumann, Gerd 4 Bläser, Markus 4 Borwein, Peter Benjamin 4 Bugeaud, Yann 4 Cheon, Jung Hee 4 Covanov, Svyatoslav 4 Demmel, James Weldon 4 Erdős, Pál 4 Gao, Shuhong 4 Grandjean, Etienne 4 Grau, José María 4 Kim, Minkyu 4 Loui, Michael C. 4 Moreno-Centeno, Erick 4 Munro, J. Ian 4 Nagasaka, Kosaku 4 Nart, Enric 4 Oller-Marcén, Antonio M. 4 Saff, Edward Barry 4 Sedjelmaci, Sidi Mohamed 4 Sorenson, Jonathan P. 4 Varga, Richard Steven 4 Zuiddam, Jeroen 3 Bauch, Jens-Dietrich 3 Bernstein, Daniel Julius 3 Brent, Richard Peirce 3 Carnicer, Jésus Miguel 3 Chen, Ke 3 Conner, Austin 3 Cook, Stephen Arthur 3 Coxon, Nicholas 3 Dujella, Andrej 3 Dymond, Patrick W. 3 Ehlich, Hartmut 3 Escobedo, Adolfo R. 3 Ezome, Tony 3 Ford, Kevin B. 3 Freeden, Willi 3 Fürer, Martin 3 Gemignani, Luca 3 Gesmundo, Fulvio 3 Haverkamp, Richard G. 3 Ibrahimoglu, Bayram Ali 3 Iliopoulos, Costas S. 3 Jank, Gerhard 3 Khalil, Omar A. 3 Khiar, Yasmina 3 Kochergin, Vadim Vasil’evich 3 Lercier, Reynald 3 Maier, Helmut 3 Maynard, James 3 Michałek, Mateusz 3 Okša, Gabriel 3 Panario, Daniel 3 Pauli, Sebastian 3 Pejković, Tomislav 3 Peña, Juan Manuel 3 Poteaux, Adrien 3 Rack, Heinz-Joachim 3 Romani, Francesco 3 Saurabh, Saket 3 Shoup, Victor 3 Shparlinski, Igor E. ...and 1,016 more Authors all top 5 Cited in 191 Serials 67 Theoretical Computer Science 64 Mathematics of Computation 61 Journal of Symbolic Computation 42 Journal of Approximation Theory 41 Information Processing Letters 24 Linear Algebra and its Applications 23 Journal of Complexity 21 Journal of Computational and Applied Mathematics 21 Numerische Mathematik 14 Computational Complexity 13 Computers & Mathematics with Applications 13 Journal of Computer and System Sciences 12 Algorithmica 11 Journal of Number Theory 10 Discrete Applied Mathematics 10 Computing 9 BIT 8 Applicable Algebra in Engineering, Communication and Computing 7 Discrete Mathematics 7 Mathematische Zeitschrift 7 Random Structures & Algorithms 7 Experimental Mathematics 6 Journal of Soviet Mathematics 6 Information and Computation 6 SIAM Journal on Matrix Analysis and Applications 6 LMS Journal of Computation and Mathematics 6 Foundations of Computational Mathematics 5 Acta Informatica 5 Journal of Pure and Applied Algebra 5 Applied Numerical Mathematics 5 Designs, Codes and Cryptography 5 Annals of Mathematics. Second Series 5 Proceedings of the Steklov Institute of Mathematics 4 Mathematical Notes 4 Calcolo 4 Mathematical Systems Theory 4 Monatshefte für Mathematik 4 Journal of Cryptology 4 Numerical Algorithms 4 RAIRO. Informatique Théorique et Applications 4 Journal de Théorie des Nombres de Bordeaux 4 Journal of Mathematical Sciences (New York) 4 Journal of Discrete Algorithms 4 Prikladnaya Diskretnaya Matematika 3 Moscow University Mathematics Bulletin 3 Advances in Mathematics 3 Archiv der Mathematik 3 Journal of Algebra 3 Programming and Computer Software 3 SIAM Journal on Computing 3 Combinatorica 3 Bulletin of the American Mathematical Society. New Series 3 Cybernetics and Systems Analysis 3 Finite Fields and their Applications 3 Theory of Computing Systems 3 BIT. Nordisk Tidskrift for Informationsbehandling 2 International Journal of Control 2 International Journal of Theoretical Physics 2 Periodica Mathematica Hungarica 2 Applied Mathematics and Computation 2 Journal of Combinatorial Theory. Series A 2 Manuscripta Mathematica 2 Mathematische Annalen 2 Mathematics and Computers in Simulation 2 Mathematica Slovaca 2 Numerical Functional Analysis and Optimization 2 Proceedings of the American Mathematical Society 2 Proceedings of the Edinburgh Mathematical Society. Series II 2 Transactions of the American Mathematical Society 2 Constructive Approximation 2 Discrete & Computational Geometry 2 Revista Matemática Iberoamericana 2 Journal of the American Mathematical Society 2 Journal of Scientific Computing 2 The Annals of Applied Probability 2 International Journal of Foundations of Computer Science 2 Discrete Mathematics and Applications 2 Computational Mathematics and Mathematical Physics 2 International Journal of Computer Mathematics 2 Mathematical Programming. Series A. Series B 2 Journal of the ACM 2 Journal of Discrete Mathematical Sciences & Cryptography 2 The Journal of Logic and Algebraic Programming 2 Natural Computing 2 Parallel Processing Letters 2 International Journal of Number Theory 2 Chebyshevskiĭ Sbornik 2 ACM Communications in Computer Algebra 2 Algorithms 2 Research in Number Theory 1 Acta Mathematica Academiae Scientiarum Hungaricae 1 American Mathematical Monthly 1 Bulletin of the Australian Mathematical Society 1 Communications in Mathematical Physics 1 Journal d’Analyse Mathématique 1 Journal of Mathematical Analysis and Applications 1 Journal of Mathematical Physics 1 Journal of Statistical Physics 1 The Mathematical Gazette 1 Mathematical Methods in the Applied Sciences ...and 91 more Serials all top 5 Cited in 47 Fields 429 Computer science (68-XX) 233 Number theory (11-XX) 231 Numerical analysis (65-XX) 91 Approximations and expansions (41-XX) 67 Linear and multilinear algebra; matrix theory (15-XX) 65 Field theory and polynomials (12-XX) 52 Information and communication theory, circuits (94-XX) 47 Combinatorics (05-XX) 43 Commutative algebra (13-XX) 42 Algebraic geometry (14-XX) 35 Functions of a complex variable (30-XX) 22 Mathematical logic and foundations (03-XX) 20 Operations research, mathematical programming (90-XX) 13 Group theory and generalizations (20-XX) 13 Harmonic analysis on Euclidean spaces (42-XX) 13 Quantum theory (81-XX) 11 Real functions (26-XX) 9 Special functions (33-XX) 8 History and biography (01-XX) 8 Probability theory and stochastic processes (60-XX) 7 Associative rings and algebras (16-XX) 7 Ordinary differential equations (34-XX) 7 Partial differential equations (35-XX) 5 General and overarching topics; collections (00-XX) 5 Dynamical systems and ergodic theory (37-XX) 5 Statistics (62-XX) 4 Order, lattices, ordered algebraic structures (06-XX) 4 Functional analysis (46-XX) 4 Operator theory (47-XX) 4 Statistical mechanics, structure of matter (82-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Sequences, series, summability (40-XX) 2 General algebraic systems (08-XX) 2 Integral transforms, operational calculus (44-XX) 2 Fluid mechanics (76-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Difference and functional equations (39-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral equations (45-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Convex and discrete geometry (52-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Mechanics of particles and systems (70-XX) 1 Geophysics (86-XX) 1 Systems theory; control (93-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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