diplom.bib

@comment{Wurzel-/Anfangsverweise der Diplomarbeit}

@inproceedings
{   Csan76,
    author    = {L. Csanky},
    title     = {Fast {P}arallel {M}atrix {I}nversion {A}lgorithms},
    booktitle = {Siam Journal on Computing},
    year      = {1976},
    pages     = {618-623}
}

@inproceedings
{   BGH82,
    author    = {A. Borodin and J. von zur Gathen and J. Hopcroft},
    title     = {Fast {P}arallel {M}atrix and {GCD} {C}omputation},
    booktitle = {Information and Control 52},
    year      = {1982},
    pages     = {241-256}
}

@inproceedings
{   BGH82a,
    author    = {A. Borodin and J. von zur Gathen and J. Hopcroft},
    title     = {Fast {P}arallel {M}atrix and {GCD} {C}omputations},
    booktitle = {IEEE Foundations of Computer Science},
    year      = {1982},
    pages     = {65-71}
}
 
@inproceedings
{   Berk84,
    author    = {S. J. Berkowitz},
    title     = {{On Computing the Determinant in Small Parallel Time Using
                a Small Number of Processors}},
    booktitle = {Information Processing Letters 18},
    year      = {1984},
    pages     = {147-150}
}

@inproceedings
{   Pan85,
    author    = {V. Pan},
    title     = {{Fast and Efficient Parallel Algorithms for the 
                 Exact
                 Inversion of Integer Matrices}},
    booktitle = {Lecture Notes on Computer Science 206},
    year      = {1985},
    pages     = {504-521}
}



@comment{ selbst beschaffte Literaturstellen: }

@comment{ effiziente Matrizenmultiplikation }
@inproceedings
{   CW90,
    author    = {D. Coppersmith and S. Winograd},
    title     = {{Matrix Multiplikation via Arithmetic Progressions}},
    booktitle = {Journal of Symbolic Computation 9},
    year      = 1990,
    pages     = {251-280}
}

@comment{ Beschreibung von 'VSBR83' ab S. 22; 
          sollte 'masterthesis' sein, dieser Typ ist in der Style-Datei
          jedoch nicht bekannt }
@misc
{   Wald87,
    author  = {I. Wald},
    title   = {{Automatische Parallelisierung von Registermaschinen}},
    note    = { Diplomarbeit, Johann Wolfgang Goethe-Universit"at,
                Frankfurt am Main
              },
    year    = 1987
}


@comment{ selbst gefundene Literaturstellen: }

@book
{
    DCLR86,
    author  = {M. Dal Cin and J. Lutz and T. Risse},
    title = {{Programmierung in Modula-2}},
    edition = {2.},
    publisher = {Teubner Verlag},
    year = 1986
}

@comment{ BGH82 -> Konvergenz von Potenzreihen mit mehreren Unbestimmten: 
                   S. 1 ff, 49 ff }
@book
{
    BT70,
    author    = {H. Behnke and P. Thullen},
    title     = {{Theorie der Funktionen mehrerer komplexer
                  Ver"anderlicher}},
    publisher = {Springer Verlag},
    year      = 1970
}

@comment{ BGH82 -> Konvergenz von Potenzreihen mit mehreren Unbestimmten:
                   S. 34 ff; Vornahme des Autors: Lars}
@book
{
    Hoer73,
    author    = {L. H"orsmander},
    title     = {{An Introduction to Complex Analysis in Several
                  Variables}},
    publisher = {North Holland Publishing Company},
    year      = 1973
}

@comment{ Zurm64 -> Verfahren von Krylov;
          Abk"urzung von 'booktitle': Bull. Acad. Sci. URSS }
@inproceedings
{   Kryl31,
    author    = {A. N. Krylov},
    title     = {{ 7. Ser. Classe Mathem. }},
    booktitle = {Bulletins of the Academie of Sciences of URSS},
    year      = 1931,
    pages     = {491-538}
}

@comment{ Berk84 -> numerische Integration zur Absch"atzung der Anzahl
                    der Prozessoren }
@book
{   EM88,
    author    = {G. Engeln-M"ullges and F. Reutter},
    title     = {{Formelsammlung zur Numerischen Mathematik mit 
                  Modula2-Programmen}},
    publisher = {BI-Wissenschaftsverlag},
    year      = 1988
}

@comment{ PR85 -> Hous64; Methode von Leverrier (S. 166; BM b351/Hous);
          'book', jedoch 'publisher' fehlt }
@misc
{   Hous64,
    author    = {A. Housholder},
    title     = {{The Theory of Matrices in Numerical Analysis}},
    year      = 1964
}

@comment{ Beweis f"ur `Newton'sche Gleichungen f"ur Potenzsummen' in
          Kapitel 8 (S. 181); sollte 'book' sein, jedoch 'publisher' fehlt }
@misc
{   Haup52,
    author    = {O. Haupt},
    title     = {{Einf"uhrung in die Algebra}},
    volume    = {Band 1},
    edition   = {2. Auflage},
    address   = {Leipzig},
    year      = 1952
}

@comment{ Beweise f"ur S"atze von Frame pp. 225-235: }
@book
{   Dwye51,
    author    = {P. S. Dwyer},
    title     = {{Linear Computations}},
    publisher = {John Wiley and Sons},
    address   = {New York},
    year      = 1951
}

@comment{Beweis f"ur Taylorentwicklung (pp.33-35); 
         sollte 'book' sein, jedoch fehlt 'publisher'}
@misc
{   Hild74,
    author    = {F. B. Hildebrand},
    title     = {{Introduction to Numerical Analysis}},
    edition   = {2nd Edition},
    year      = 1974
}

@comment{sollte 'book' sein; jedoch fehlt 'publisher'}
@misc
{   Mang67,
    author    = {H. von Mangoldt},
    title     = {{Einf"uhrung in die h"ohere Mathematik}},
    volume    = {Band 3},
    year      = 1967
}

@book
{   Doer77,
    author    = {W. D"orfler},
    title     = {Mathematik f"ur Informatiker},
    volume    = {Band 1},
    publisher = {Hanser Verlag},
    year      = 1977
}

@book
{   Sieb80,
    author    = {H. Sieber and L. Huber},
    title     = {{Mathematische Formeln}},
    publisher = {Verlag Ernst Klett},
    address   = {Stuttgart},
    year      = {1980}
}

@book
{   BS86,
    author    = {I. N. Bronstein and K. A. Semendjajew},
    title     = {{Taschenbuch der Mathematik, Erg"anzende Kapitel}},
    publisher = {Verlag Harri Deutsch},
    address   = {Thun und Frankfurt/Main},
    edition   = {4.},
    year      = 1986
}

@book
{   BS87,
    author    = {I. N. Bronstein and K. A. Semendjajew},
    title     = {{Taschenbuch der Mathematik}},
    publisher = {Verlag Harri Deutsch},
    address   = {Thun und Frankfurt/Main},
    edition   = {23.},
    year      = {1987}
}

@booklet
{   Simula85,
    key       = {Simula85},
    title     = {{SIMULA Standard}},
    month     = {{J}uli},
    year      = {1985},
    note      = {The SIMULA Standards Group}
}    

@book
{   Wege89,
    author    = {I. Wegener},
    title     = {{Effiziente Algorithmen f"ur grundlegende Funktionen}},
    publisher = {B. G. Teubner},
    address   = {Stuttgart},
    year      = {1989}
}

@book
{   Elli82,
    author    = {D. F. Elliott},
    title     = {Fast Transforms},
    publisher = {Academic Press},
    year      = {1982}
}

@misc
{   Wegn80,
    author       = {G. Wegner},
    title        = {{Lineare Algebra f"ur Informatiker 1}},
    howpublished = {Vorlesungsskript},
    year         = {1980},
    note         = {{Universit"at Dortmund}}
}
   
@book
{   Rao65,
    author    = {C. R. Rao},
    title     = {{Linear Statistical Inference and its Applications}},
    publisher = {Wiley},
    year      = {1968},
    note      = {2nd corr. print}
}

@book
{   DLR86,
    author    = {M. Dal Cin and J. Lutz and T. Risse},
    title     = {{P}rogrammierung in {M}odula-2},
    publisher = {Teubner},
    year      = {1986},
    note      = {2., "uberarbeitete Auflage}
}

@comment{'Isaa73' sollte eigentlich 'IK73' sein}
@comment{'misc' sollte eigentlich 'book' sein, aber 'publisher' fehlt}
@misc
{   Isaa73,
    author    = {E. Isaacson and H. B. Keller},
    title     = {{Analyse numerischer Verfahren}},
    year      = 1973
}

@book
{   Achi67,
    author    = {N. I. Achieser},
    title     = {{Vorlesungen "uber Approximationstheorie}},
    publisher = {Akademie-Verlag},
    address   = {Berlin},
    year      = 1967
}

@comment{'misc' sollte eigentlich 'book sein, aber 'publisher' fehlt}
@misc
{   Zurm64,
    author    = {R. Zurm"uhl},
    title     = {{Matrizen}},
    year      = 1964
}


@comment{Literaturverweise in 'Csan76'}

@phdthesis
{   Csan74,
    author   = {L. Csanky},
    title    = {{On the Parallel Complexity of Some Computational Problems}},
    school   = {Computer Science Division, University of California, 
                Berkeley},
    year     = {1974}
}

@book
{   FF63,
    author    = {D. K. Faddeev and V. N. Faddeeva},
    title     = {Computational {M}ethods of {L}inear {A}lgebra},
    publisher = {W. H. Freeman},
    address   = {San Francisco},
    year      = {1963}
}

@book
{   FF76,
    author    = {D. K. Faddeev and V. N. Faddeeva},
    title     = {{Computational Methods of Linear Algebra}},
    publisher = { },
    year      = {1976}
}

@inproceedings
{   Fram49,
    author    = {J. S. Frame},
    title     = {{A Simple Recurrent Formula for Inverting a Matrix}},
    booktitle = {Bulletins of the American Mathematic Society 55},
    year      = {1949},
    pages     = {1045}
}

@techreport
{   Hell73,
    author      = {D. Heller},
    title       = {{A Determinant Theorem With Applications to Parallel 
                   Algorithms}},
    institution = {Department of Computer Science, Carnegie-Mellon
                   University, Pittsburgh},
    year        = {1973}
}

@book
{   MM64,
    author    = {M. Marcus and H. Ming},
    title     = {A {S}urvey of {M}atrix {T}heory and {M}atrix {I}nequalities},
    publisher = {Allyn and Bacon},
    address   = {Boston},
    year      = {1964}
}



@comment{Literaturverweise in 'BGH82'}

@inproceedings
{   Bare68,
    author    = {H. E. Bareiss},
    title     = {{Sylvester's Identity and Multistep Integer-Preserving 
                 Gaussian Elimination}},
    booktitle = {Math. Comput. 22},
    year      = {1968},
    pages     = {565-578}
}

@comment{Abk"urzung f"ur 'booktitle' war 'Theor. Comp. Sci.'...:}
@inproceedings
{   BS83,
    author    = {W. Baur and V. Strassen},
    title     = {{The computational complexity of partial derivatives}},
    booktitle = {Theoretical Computer Science},
    year      = {1983},
    pages     = {317-330}
}

@comment{booktitle = {Math. Comput. 24}
@inproceedings
{   Berl70,
    author    = {E. R. Berlekamp},
    title     = {{Factoring Polynomials Over Large Fields}},
    booktitle = {Mathematics Computations 24},
    year      = {1970},
    pages     = {713-735}
}

@comment{Berk84}

@inbook
{   Boro82,
    author    = {A. Borodin},
    title     = {{Logic and Algorithmic, Symposium in Honour of Ernst
                 Specker}},
    chapter   = {{Structured vs. General Models in Computational Complexity}},
    pages     = {47-65},
    publisher = {l'Enseignement Math\'ematique},
    year      = {1982},
    comment   = {nicht sicher, ob 'inbook' richtig}
}

@comment{Csan76}

@comment{booktitle= J. Res. Nat. Bur. Stand. 71B (4)}
@inproceedings
{   Edmo67,
    author    = {J. Edmonds},
    title     = {{Systems of Distinct Representatives and Linear Algebra}},
    booktitle = {J. Res. Nat. Bur. Stand. 71B (4)},
    year      = {1967},
    pages     = {241-245}
}

@misc
{   Feat81,
    author       = {T. Feather},
    howpublished = {Private communication},
    year         = {1981},
    month        = {11.}
}

@inproceedings
{   FN44,
    author    = {N. J. Fine and I. Niven},
    title     = {The probability that a determinant be congruent 
                 to a (mod m)},
    booktitle = {Bulletins of the American Mathematic Society 50},
    year      = {1944},
    pages     = {89-93}
}

@inproceedings
{   FW78,
    author    = {S. Fortune and J. Wyllie },
    title     = {Parallelism in ramdom access machines},
    booktitle = {Proc. 10th ACM Symp. Theory of Computing},
    year      = {1978},
    pages     = {114-118},
    address   = {San Diego, California}
}

@inproceedings 
{   Gath83,
    author    = {J. von zur Gathen},
    title     = {Parallel algorithms for algebraic problems},
    booktitle = {Proc. 15th ACM Symp. Theory of Computing},
    year      = {1983},
    address   = {Boston}
}

@inproceedings
{   GSS82,
    author    = {L. M. Goldschlager and R. A. Shaw and J. Staples},
    title     = {The maximum flow problem is log space complete for {P}},
    booktitle = {Theor. Comput. Sci. 21},
    year      = {1982},
    pages     = {105-111}
}

@book
{   Henr77,
    author    = {P. Henrici},
    title     = {Applied and {C}omputational {C}omplex {A}nalysis},
    publisher = {Wiley},
    year      = {1977},
    volume    = {2},
    address   = {New York}
}

@inproceedings
{   IMR80,
    author    = {O. Ibarra and S. Morgan and L. E. Rosier},
    title     = {A note on the parallel complexity of computing the rank of
                 order n matrices},
    booktitle = {Information Processing Letters 11},
    year      = {1980},
    pages     = {162}
}

@inproceedings
{   Jord11,
    author    = {C. Jordan},
    title     = {Sur le nombre des solutions de la congruence
                 $ |a_{ik}| \equiv {A} \pmod{ M } $},
    booktitle = {J. Math. Pures Appl (6), 7},
    year      = {1911},
    pages     = {409-416}
}

@inproceedings
{   Pipp79,
    author    = {N. Pippenger},
    title     = {On simultameous resource bounds},
    booktitle = {Proc. IEEE 20th Annual FOCS},
    year      = {1979},
    month     = {October},
    pages     = {307-311}
}

@inproceedings
{   Rabi80,
    author    = {M. O. Rabin},
    title     = {Probabilistic algorithms in finite fields},
    booktitle = {SIAM J. Comput. 9},
    year      = {1980},
    pages     = {273-280}
}

@book
{   Rotm73,
    author    = {J. J. Rotman},
    title     = {The {T}heory of {G}roups},
    publisher = {Allyn & Bacon},
    year      = {1973},
    address   = {Boston},
    edition   = {2}
}

@inproceedings
{   Stra73,
    author    = {V. Strassen},
    title     = {Vermeidung von {D}ivisionen},
    booktitle = {J. Reine Angew. Math. 264},
    year      = {1973},
    pages     = {184-202}
}

@inproceedings
{   VSBR83,
    author    = {L. Valiant and S. Skyum and S. Berkowitz and C. Rackoff},
    title     = {{Fast Parallel Computation of Polynomials Using Few 
                 Processors}},
    booktitle = {SIAM Journal on Computing 12 (4)},
    pages     = {641-644},
    year      = {1983}
}

@inbook
{   Vali82,
    author    = {L. Valiant},
    title     = {Logic and {A}lgorithmic, {S}ymposium in {H}onour of
                 {E}rnst {S}pecker},
    chapter   = {Reducibility by algebraic projections},
    pages     = {365-380},
    publisher = {l'Enseignement Math\'ematique},
    year      = {1982},
    volume    = {30},
    comment   = {nicht sicher ob 'inbook' richtig}
}



@comment{Literaturverweise in 'Berk84'}

@book
{   AHU74,
    author    = {A. V. Aho and J. Hopcroft and J. D. Ullman},
    title     = {The {D}esign and {A}nalysis of {C}omputer {A}lgorithms},
    publisher = {Addison-Wesley},
    year      = {1974}
}

@misc
{   Beam82,
    author       = {P. Beame},
    howpublished = {Private communication},
    year         = {1982}
}

@comment{BGH82}

@inproceedings
{   CW81,
    author    = {D. Coppersmith and S. Winograd},
    title     = {{On the Asymptotic Complexity of Matrix Multiplication}},
    booktitle = {Proceedings of the 
                 22nd Symposium on Foundations of Computer Science},
    year      = {1981},
    pages     = {82-90}
}

@comment{Csan76}

@comment{FF63}

@comment{booktitle = J. ACM 27}
@inproceedings
{   LF80,
    author    = {R. Ladner and M. Fischer},
    title     = {{Parallel Prefix Computations}},
    booktitle = {Journal of the ACM 27},
    year      = {1980},
    pages     = {831-838}
}

@comment{booktitle= Ann. Math. Statist.}
@inproceedings
{   Samu42,
    author    = {P. A. Samuelson},
    title     = {{A Method for Determining Explicitly the Coefficients of
                 the Characteristic Equation}},
    booktitle = {Annals of Mathematical Statistics 13},
    year      = {1942},
    pages     = {424-429}
}

@comment{VBSR83}

@misc
{   Wino82,
    author       = {S. Winograd},
    howpublished = {Private communication},
    year         = {1982}
}



@comment{Literaturverweise in 'Pan85'}

@comment{Berk84}

@inproceedings
{   BP,
    author    = {D. Bini and V. Pan},
    title     = {Fast {P}arallel {P}olynomial {D}ivision via {R}eduction to
                {T}riangular {T}oeplitz {M}atrix {I}nversion and to
                {P}olynomial {I}nversion {M}odulo a {P}ower},
    booktitle = {to appear in Information Processing Letters}
}

@inproceedings
{   BCP83,
    author    = {A. Borodin and S. Cook and N. Pippenger},
    title     = {Parallel {C}omputation for {W}ell-{E}ndowed {R}ings and 
                 {S}pace-{B}ounded {P}robabilistic {Machines}},
    booktitle = {Information and Control 58},
    year      = {1983},
    pages     = {113-136}
}

@comment{BGH82 and BGH82a}

@book
{   BM75,
    author    = {A. Borodin and I. Munro},
    title     = {{The Computational Complexity of Algebraic and Numeric
                  Problems}},
    publisher = {American Elsevier},
    year      = {1975},
    address   = {New York}
}

@inproceedings
{   CW82,
    author    = {D. Coppersmith and S. Winograd},
    title     = {{On the Asymptotic Complexity of Matrix Multiplication}},
    booktitle = {SIAM J. on Computing 11 (3)},
    year      = {1982},
    pages     = {472-492}
}

@comment{Csan76}

@inproceedings
{   Eber84,
    author    = {W. Eberly},
    title     = {{Very Fast Parallel Matrix and Polynomial Arithmetic}},
    booktitle = {Proc. 25-th Ann. IEEE Symp. FOCS},
    year      = {1984},
    pages     = {21-30}
}

@techreport
{   GP85,
    author      = {Z. Galil and V. Pan},
    title       = {{Fast and Efficient Parallel Computation of Perfect
                    Matching}},
    institution = {Columbia University, N. Y.},
    year        = {1985},
    month       = {March}
}

@inproceedings
{   Gath84,
    author    = {I. von zur Gathen},
    title     = {{Parallel Algorithms for Algebraic Problems}},
    booktitle = {SIAM J. on Computing 13 (4)},
    year      = {1984},
    pages     = {802-824}
}

@book
{   GL83,
    author    = {G. H. Golub and C. F. van Loan},
    title     = {{Matrix Computation}},
    publisher = {The John Hopkins University Press},
    year      = {1983},
    address   = {Baltimore}
}

@book
{   IR82,
    author    = {K. Ireland and M. Rosen},
    title     = {{ A Classical Introduction to Modern Number Theory}},
    publisher = {Springer-Verlag},
    year      = {1982}
}

@misc
{   Kell82,
    author    = {W. Keller},
    title     = {{Fast Algorithms for the Characteristic Polynomial}},
    note      = {{Diplomarbeit, Institut f"ur Angewandte Mathematik, 
                  Univ. Z"urich}},
    year      = 1982
}

@book
{   Knut81,
    author    = {D. E. Knuth},
    title     = {{The Art of Computer Programming: Seminumerical 
                  Algorithms}},
    publisher = {Addison-Wesley},
    year      = {1981},
    volume    = {2}
}

@comment{MM64}

@inproceedings
{   MC79,
    author    = {R. T. Moenck and J. H. Carter},
    title     = {{Approximate Algorithms to Derive Exact Solutions to 
                  Systems of Linear Equations}},
    booktitle = {Proc. EUROSAM 1979, Lecture Notes in Computer Science 72},
    year      = {1979},
    pages     = {63-73},
    publisher = {Springer}
}

@techreport
{   Pan80,
    author      = {V. Pan},
    title       = {{The Bit-Complexity of the Convolution of Vectors and of 
                    the DFT}},
    institution = {Computer Science Dept.},
    year        = {1980},
    number      = {TR-80-6},
    address     = {SUNY Albany, New York},
    month       = {May}
}

@inproceedings
{   Pan84,
    author      = {V. Pan},
    title       = {How to Multiply Matrices Faster},
    booktitle   = {Lecture Notes in Computer Science 179},
    year        = {1984},
    publisher   = {Springer-Verlag},
    address     = {Berlin}
}

@techreport
{   Pan84a,
    author      = {V. Pan},
    title       = {The Bit Complexity of Matrix Multiplication and of 
                   Related Computational Problems in Linear Algebra. 
                   The Segmented $\lambda$ Algorithms},
    institution = {Dept. of Informatica, University of Pisa},
    year        = {1984},
    address     = {Italy},
    month       = {August},
    note        = {to appear in Computers and Mathematics (with
                   Applications)}
}

@comment{ kein Verweis hierauf; gek"urzte Version von PR85a }
@inproceedings
{   PR85,
    author    = {V. Pan and J. Reif},
    title     = {{Efficient Parallel Solution of Linear Systems}},
    booktitle = {{Proceedings of the 17th Annual ACM Symposium on 
                  Theory of Computing}},
    year      = 1985,
    pages     = {143-152}
} 

@techreport
{   PR85a,
    author      = {V. Pan and J. Reif},
    title       = {Fast and Efficient Parallel Solution of Linear Systems},
    institution = {Center for Research in Computer Technology},
    year        = {1985},
    number      = {TR-02-85},
    address     = {Aiken Computation Laboratory, Harvard University}
}

@comment{ PR85, PR85a  -->  Atki78 S. 416-431 }
@book
{   Atki78,
    author    = {K. E. Atkinson},
    title     = {{An Introduction to Numerical Analysis}},
    publisher = {Wiley},
    year      = 1978,
    address   = {New York}
}

@inproceedings
{   PS78,
    author      = {F. P. Preparata and D. V. Sarwate},
    title       = {An Improved Parallel Processor Bound in Fast Matrix
                   Inversion},
    booktitle   = {Information Processing Letters 7 (3)},
    year        = {1978},
    pages       = {148-149}
}

@book
{   Sava76,
    author      = {J. E. Savage},
    title       = {The Complexity of Computing},
    publisher   = {John Wiley and Sons},
    year        = {1976},
    address     = {New York}
}

@inproceedings
{   Schw80,
    author      = {J. T. Schwartz},
    title       = {Fast Probabilistic Algorithms for Verification of 
                   Polynomial Identities},
    booktitle   = {J. of ACM 27 (4)},
    year        = {1980},
    pages       = {701-717}
}

@book
{   Wilk65,
    author      = {J. H. Wilkinson},
    title       = {The Algebraic Eigenvalue Problem},
    publisher   = {Clareodon Press},
    year        = {1965},
    address     = {Oxford}
}

@inproceedings
{   Yun76,
    author      = {D. Y. Y. Yun},
    title       = {Algebraic Algorithms Using p-adic Constructions},
    booktitle   = {Proc. ACM Symp. Symbolic and Algebraic Computation},
    year        = {1976},
    pages       = {248-259}
}


@comment{Literaturverweise in 'Stra73' (unvollst"andig)}

@comment{book, jedoch publisher unbekannt}
@misc
{   Bour67,
    author      = {N. Bourbaki},
    title       = {{El\'ements de Math\'ematique, Livre 2, Alg\`ebre}},
    year        = 1967
}


@comment{Literaturverweise in 'Csan74' (unvollst"andig)}

@comment{Csan74, Seite 45:}

@misc
{   Munr,
    author      = {I. Munro},
    note        = {{Private Communication}}
}

@book
{   Bode59,
    author      = {E. Bodewig},
    title       = {{Matrix Calculus}},
    publisher   = {{North-Holland Pub. Co.}},
    year        = 1959
}