74,325 research outputs found
Algorithms for solving inverse geophysical problems on parallel computing systems
For solving inverse gravimetry problems, efficient stable parallel algorithms based on iterative gradient methods are proposed. For solving systems of linear algebraic equations with block-tridiagonal matrices arising in geoelectrics problems, a parallel matrix sweep algorithm, a square root method, and a conjugate gradient method with preconditioner are proposed. The algorithms are implemented numerically on a parallel computing system of the Institute of Mathematics and Mechanics (PCS-IMM), NVIDIA graphics processors, and an Intel multi-core CPU with some new computing technologies. The parallel algorithms are incorporated into a system of remote computations entitled "Specialized Web-Portal for Solving Geophysical Problems on Multiprocessor Computers." Some problems with "quasi-model" and real data are solved. Β© 2013 Pleiades Publishing, Ltd
Parallel stable compactification for ODE with parameters and multipoint conditions
Many algorithms for solving ordinary dierential equations with parameters and multipoint side conditions give rise to systems of linear algebraic equations in which the coecient matrices have a bordered block diagonal structure. In this paper, we show how these problems can be solved by using parallel algorithms based on stabilized compactication.
Gaussian block algorithms for solving path problems
Path problems are a family of optimization and enumeration problems that reduce to determination or evaluation of paths in a directed graph. In this paper we give a convenient algebraic description of block algorithms for solving path problems. We also develop block versions of two Gaussian algorithms, which are counterparts of the conventional Jordan and escalator method respectively. The correctness of the two considered block
algorithms is discussed, and their complexity is analyzed. A parallel
implementation of the block Jordan algorithm on a transputer network is presented, and the obtained experimental results are listed
On Dynamic Algorithms for Algebraic Problems
In this paper, we examine the problem of incrementally evaluating algebraic functions. In particular, if f(x1, x2, β¦, xn) = (y1, y2, β¦, ym) is an algebraic problem, we consider answering on-line requests of the form "change input xi to value v" or "what is the value of output yj?" We first present lower bounds for some simply stated algebraic problems such as multipoint polynomial evaluation, polynomial reciprocal, and extended polynomial GCD, proving an &#x03A9(n). lower bound for the incremental evaluation of these functions. In addition, we prove two time-space trade-off theorems that apply to incremental algorithms for almost all algebraic functions. We then derive several general-purpose algorithm design techniques and apply them to several fundamental algebraic problems. For example, we give an O(
√ n 
) time per request algorithm for incremental DFT. We also present a design technique for serving incremental requests using a parallel machine, giving a choice of either optimal work with respect to the sequential incremental algorithm or superfast algorithms with O(log log n) time per request with a sublinear number of processors
ΠΠΏΡΠΈΠΌΡΠ·Π°ΡΡΡ ΠΏΠ°ΡΠ°Π»Π΅Π»ΡΠ½ΠΈΡ Π°Π»Π³ΠΎΡΠΈΡΠΌΡΠ² ΡΠΎΠ·Π²βΡΠ·ΡΠ²Π°Π½Π½Ρ Π·Π°Π΄Π°Ρ Π· ΡΠΎΠ·ΡΡΠ΄ΠΆΠ΅Π½ΠΈΠΌΠΈ ΠΌΠ°ΡΡΠΈΡΡΠΌΠΈ
Π ΠΎΠ·Π³Π»ΡΠ΄Π°ΡΡΡΡΡ ΠΏΡΠΎΠ±Π»Π΅ΠΌΠΈ ΠΎΡΠ³Π°Π½ΡΠ·Π°ΡΡΡ ΠΎΠ±ΡΠΈΡΠ»Π΅Π½Π½Ρ ΡΠΎΠ·Π²βΡΠ·ΠΊΡΠ² ΡΠΈΡΡΠ΅ΠΌ Π»ΡΠ½ΡΠΉΠ½ΠΈΡ
Π°Π»Π³Π΅Π±ΡΠ°ΡΡΠ½ΠΈΡ
ΡΡΠ²Π½ΡΠ½Ρ ΡΠ° ΡΠ°ΡΡΠΊΠΎΠ²ΠΎΡ ΡΠ·Π°Π³Π°Π»ΡΠ½Π΅Π½ΠΎΡ Π°Π»Π³Π΅Π±ΡΠ°ΡΡΠ½ΠΎΡ ΠΏΡΠΎΠ±Π»Π΅ΠΌΠΈ Π²Π»Π°ΡΠ½ΠΈΡ
Π·Π½Π°ΡΠ΅Π½Ρ Π· ΡΠΎΠ·ΡΡΠ΄ΠΆΠ΅Π½ΠΈΠΌΠΈ ΡΠΈΠΌΠ΅ΡΡΠΈΡΠ½ΠΈΠΌΠΈ ΠΌΠ°ΡΡΠΈΡΡΠΌΠΈ. ΠΠ°ΠΏΡΠΎΠΏΠΎΠ½ΠΎΠ²Π°Π½ΠΎ ΠΌΠΎΠ΄ΠΈΡΡΠΊΠ°ΡΡΡ ΠΏΠ°ΡΠ°Π»Π΅Π»ΡΠ½ΠΈΡ
Π°Π»Π³ΠΎΡΠΈΡΠΌΡΠ² ΡΠΎΠ·Π²βΡΠ·ΡΠ²Π°Π½Π½Ρ ΡΠΈΡΡΠ΅ΠΌ Π»ΡΠ½ΡΠΉΠ½ΠΈΡ
Π°Π»Π³Π΅Π±ΡΠ°ΡΡΠ½ΠΈΡ
ΡΡΠ²Π½ΡΠ½Ρ Π· ΡΠΎΠ·ΡΡΠ΄ΠΆΠ΅Π½ΠΈΠΌΠΈ ΡΡΠΈΠΊΡΡΠ½ΠΈΠΌΠΈ ΠΌΠ°ΡΡΠΈΡΡΠΌΠΈ Π΄Π»Ρ ΠΏΡΠ΄Π²ΠΈΡΠ΅Π½Π½Ρ Π΅ΡΠ΅ΠΊΡΠΈΠ²Π½ΠΎΡΡΡ ΡΠΎΠ·ΠΏΠ°ΡΠ°Π»Π΅Π»ΡΠ²Π°Π½Π½Ρ.Π Π°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°ΡΡΡΡ ΠΏΡΠΎΠ±Π»Π΅ΠΌΡ ΠΎΡΠ³Π°Π½ΠΈΠ·Π°ΡΠΈΠΈ Π²ΡΡΠΈΡΠ»Π΅Π½ΠΈΡ ΡΠ΅ΡΠ΅Π½ΠΈΠΉ ΡΠΈΡΡΠ΅ΠΌ Π»ΠΈΠ½Π΅ΠΉΠ½ΡΡ
Π°Π»Π³Π΅Π±ΡΠ°ΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡΠ°Π²Π½Π΅Π½ΠΈΠΉ ΠΈ ΡΠ°ΡΡΠΈΡΠ½ΠΎΠΉ ΠΎΠ±ΠΎΠ±ΡΠ΅Π½Π½ΠΎΠΉ Π°Π»Π³Π΅Π±ΡΠ°ΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΏΡΠΎΠ±Π»Π΅ΠΌΡ ΡΠΎΠ±ΡΡΠ²Π΅Π½Π½ΡΡ
Π·Π½Π°ΡΠ΅Π½ΠΈΠΉ Ρ ΡΠ°Π·ΡΠ΅ΠΆΠ΅Π½Π½ΡΠΌΠΈ ΡΠΈΠΌΠΌΠ΅ΡΡΠΈΡΠ½ΡΠΌΠΈ ΠΌΠ°ΡΡΠΈΡΠ°ΠΌΠΈ. ΠΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Π° ΠΌΠΎΠ΄ΠΈΡΠΈΠΊΠ°ΡΠΈΡ ΠΏΠ°ΡΠ°Π»Π»Π΅Π»ΡΠ½ΡΡ
Π°Π»Π³ΠΎΡΠΈΡΠΌΠΎΠ² ΡΠ΅ΡΠ΅Π½ΠΈΡ ΡΠΈΡΡΠ΅ΠΌ Π»ΠΈΠ½Π΅ΠΉΠ½ΡΡ
Π°Π»Π³Π΅Π±ΡΠ°ΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡΠ°Π²Π½Π΅Π½ΠΈΠΉ Ρ ΡΠ°Π·ΡΠ΅ΠΆΠ΅Π½Π½ΡΠΌΠΈ ΡΡΠ΅ΡΠ³ΠΎΠ»ΡΠ½ΡΠΌΠΈ ΠΌΠ°ΡΡΠΈΡΠ°ΠΌΠΈ Π΄Π»Ρ ΠΏΠΎΠ²ΡΡΠ΅Π½ΠΈΡ ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΠΎΡΡΠΈ ΡΠ°ΡΠΏΠ°ΡΠ°Π»Π»Π΅Π»ΠΈΠ²Π°Π½ΠΈΡ.The problems of organization of solving of the systems of linear algebraic equations and partial generalized eigenvalue algebraic problem with sparse symmetric matrices are considered. Modification of parallel algorithms of solving of the systems of linear algebraic equations with sparse triangular matrices is offered for the rise of efficiency
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