G. Lueker. Some Techniques for Solving Recurrences. Computing Surveys, Vol. 12, No. 4, December 1980.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....introduction to this section. Lagged Fibonacci generators such as that implemented in su2cor take the form of a recurrence relation. Such relations can be automatically detected using pattern recognition techniques [1] General techniques for solving linear recurrences of this type are well known [17], and closed forms for such recurrences can be computed at compile time thereby breaking loop carried dependences. In cases where RNGs are not explicitly coded as linear recurrences, other techniques must be employed. Currently we plan to develop a directive interface which can be used to ....

G. Lueker. Some Techniques for Solving Recurrences. Computing Surveys, Vol. 12, No. 4, December 1980.

....combinatorial recurrences, all the books listed in Section 18 that help in dealing with combinatorial identities and generating functions are also useful in handling recurrences. Methods for recurrences that are not amenable to generating function methods are presented in [175, 177] Lueker [264] is an introductory survey to some recurrence methods. Wimp s book [382] is concerned primarily with numerical stability problems in computing with recurrences. Such problems are important in computing values of orthogonal polynomials, for example, but seldom arise in combinatorial enumeration. ....

G. S. Lueker, Some techniques for solving recurrences, Computing Surveys, 12 (1980), 419--436.

....of Mathematica. The recurrence solver tries to determine closed forms for recurrence variables based on their recurrence system which is directly obtained from the context at the loop header. The implementation of our recurrence solver (see also Section 5) is largely based on methods described in [27, 37] and improved by our own techniques as outlined in Section 6. In general it is not possible to find closed forms for every recurrence [27] We introduce new value symbols for every unresolved variable. An unresolved variable is a recurrence variable for which no closed form can be determined. ....

George S. Lueker. Some Techniques for Solving Recurrences. ACM Computing Surveys, 12(4):419--435, December 1980.

....on top of Mathematica. The recurrence solver tries to determine closed forms for recurrence variables based on their recurrence system which is directly obtained from the program context. The implementation of our recurrence solver is largely based on methods described in (Gerlek et al. 1995; Lueker, 1980) and improved by our own techniques (Fahringer and Scholz, 1997; Fahringer and Scholz, 1999) Similar to scalar variables the array manipulation inside of loops are described by recurrences. A recurrence system over A consists of a boundary condition and a recurrence relation a(0) b; b 2 A ....

Lueker, G. S.: 1980, `Some Techniques for Solving Recurrences'. ACM Computing Surveys 12(4), 419--435.

....The use of recurrence relations is one of the classical methods in combinatorial enumeration. Some general techniques, such as the generating function method, are commonly used, and ad hoc methods are known to handle specific recurrences. For general background, we refer the reader to [15] 6] [11], and [2] Combinatorial applications can be found e.g. in [1] 3] 4] 10] and [16] An important application area of these methods is the analysis of algorithms (cf. e.g. 5] 6] 7] 8] 11] 15] and [17] Very seldom does one find explicit closed formula solutions to enumeration ....

....known to handle specific recurrences. For general background, we refer the reader to [15] 6] 11] and [2] Combinatorial applications can be found e.g. in [1] 3] 4] 10] and [16] An important application area of these methods is the analysis of algorithms (cf. e.g. 5] 6] 7] 8] [11], 15] and [17] Very seldom does one find explicit closed formula solutions to enumeration problems. It is more common that the generating function can be determined on the basis of functional equations derived from a recurrence relation. There are remarkable examples where these methods, in ....

Lueker, G. S.: Some techniques for solving recurrences, Computing Surveys, 12(1980), 419-436

....introduction to this section. Lagged Fibonacci generators such as that implemented in su2cor take the form of a recurrence relation. Such relations can be automatically detected using pattern recognition techniques [1] General techniques for solving linear recurrences of this type are well known [16], and closed forms for such recurrences can be computed at compile time thereby breaking loop carried dependences. In cases where RNGs are not explicitly coded as linear recurrences, other techniques must be employed. Currently we plan to develop a directive interface which can be used to identify ....

G. Lueker. Some Techniques for Solving Recurrences. Computing Surveys, Vol. 12, No. 4, December 1980.

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G. Lueker. Some Techniques for Solving Recurrences. Computing Surveys, Vol. 12, No. 4, December 1980.

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G. Lueker. Some Techniques for Solving Recurrences. Computing Surveys, Vol. 12, No. 4, December 1980.

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G. Lueker. Some Techniques for Solving Recurrences. Computing Surveys, Vol. 12- No. 4, December 1980.

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G. Lueker. Some Techniques for Solving Recurrences. Computing Surveys, Vol. 12, No. 4, December 1980.

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