74,325 research outputs found

    Algorithms for solving inverse geophysical problems on parallel computing systems

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    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

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    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

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    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

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    In this paper, we examine the problem of incrementally evaluating algebraic functions. In particular, if f(x1, x2, …, xn) = (y1, y2, …, 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

    ΠžΠΏΡ‚ΠΈΠΌΡ–Π·Π°Ρ†Ρ–Ρ ΠΏΠ°Ρ€Π°Π»Π΅Π»ΡŒΠ½ΠΈΡ… Π°Π»Π³ΠΎΡ€ΠΈΡ‚ΠΌΡ–Π² розв’язування Π·Π°Π΄Π°Ρ‡ Π· Ρ€ΠΎΠ·Ρ€Ρ–Π΄ΠΆΠ΅Π½ΠΈΠΌΠΈ матрицями

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    Π ΠΎΠ·Π³Π»ΡΠ΄Π°ΡŽΡ‚ΡŒΡΡ ΠΏΡ€ΠΎΠ±Π»Π΅ΠΌΠΈ ΠΎΡ€Π³Π°Π½Ρ–Π·Π°Ρ†Ρ–Ρ— обчислСння розв’язків систСм Π»Ρ–Π½Ρ–ΠΉΠ½ΠΈΡ… Π°Π»Π³Π΅Π±Ρ€Π°Ρ—Ρ‡Π½ΠΈΡ… Ρ€Ρ–Π²Π½ΡΠ½ΡŒ Ρ‚Π° часткової ΡƒΠ·Π°Π³Π°Π»ΡŒΠ½Π΅Π½ΠΎΡ— Π°Π»Π³Π΅Π±Ρ€Π°Ρ—Ρ‡Π½ΠΎΡ— ΠΏΡ€ΠΎΠ±Π»Π΅ΠΌΠΈ власних Π·Π½Π°Ρ‡Π΅Π½ΡŒ Π· Ρ€ΠΎΠ·Ρ€Ρ–Π΄ΠΆΠ΅Π½ΠΈΠΌΠΈ симСтричними матрицями. Π—Π°ΠΏΡ€ΠΎΠΏΠΎΠ½ΠΎΠ²Π°Π½ΠΎ ΠΌΠΎΠ΄ΠΈΡ„Ρ–ΠΊΠ°Ρ†Ρ–ΡŽ ΠΏΠ°Ρ€Π°Π»Π΅Π»ΡŒΠ½ΠΈΡ… Π°Π»Π³ΠΎΡ€ΠΈΡ‚ΠΌΡ–Π² розв’язування систСм Π»Ρ–Π½Ρ–ΠΉΠ½ΠΈΡ… Π°Π»Π³Π΅Π±Ρ€Π°Ρ—Ρ‡Π½ΠΈΡ… Ρ€Ρ–Π²Π½ΡΠ½ΡŒ Π· Ρ€ΠΎΠ·Ρ€Ρ–Π΄ΠΆΠ΅Π½ΠΈΠΌΠΈ Ρ‚Ρ€ΠΈΠΊΡƒΡ‚Π½ΠΈΠΌΠΈ матрицями для підвищСння СфСктивності Ρ€ΠΎΠ·ΠΏΠ°Ρ€Π°Π»Π΅Π»ΡŽΠ²Π°Π½Π½Ρ.Π Π°ΡΡΠΌΠ°Ρ‚Ρ€ΠΈΠ²Π°ΡŽΡ‚ΡΡ ΠΏΡ€ΠΎΠ±Π»Π΅ΠΌΡ‹ ΠΎΡ€Π³Π°Π½ΠΈΠ·Π°Ρ†ΠΈΠΈ вычислСния Ρ€Π΅ΡˆΠ΅Π½ΠΈΠΉ систСм Π»ΠΈΠ½Π΅ΠΉΠ½Ρ‹Ρ… алгСбраичСских ΡƒΡ€Π°Π²Π½Π΅Π½ΠΈΠΉ ΠΈ частичной ΠΎΠ±ΠΎΠ±Ρ‰Π΅Π½Π½ΠΎΠΉ алгСбраичСской ΠΏΡ€ΠΎΠ±Π»Π΅ΠΌΡ‹ собствСнных Π·Π½Π°Ρ‡Π΅Π½ΠΈΠΉ с Ρ€Π°Π·Ρ€Π΅ΠΆΠ΅Π½Π½Ρ‹ΠΌΠΈ симмСтричными ΠΌΠ°Ρ‚Ρ€ΠΈΡ†Π°ΠΌΠΈ. ΠŸΡ€Π΅Π΄Π»ΠΎΠΆΠ΅Π½Π° модификация ΠΏΠ°Ρ€Π°Π»Π»Π΅Π»ΡŒΠ½Ρ‹Ρ… Π°Π»Π³ΠΎΡ€ΠΈΡ‚ΠΌΠΎΠ² Ρ€Π΅ΡˆΠ΅Π½ΠΈΡ систСм Π»ΠΈΠ½Π΅ΠΉΠ½Ρ‹Ρ… алгСбраичСских ΡƒΡ€Π°Π²Π½Π΅Π½ΠΈΠΉ с Ρ€Π°Π·Ρ€Π΅ΠΆΠ΅Π½Π½Ρ‹ΠΌΠΈ Ρ‚Ρ€Π΅ΡƒΠ³ΠΎΠ»ΡŒΠ½Ρ‹ΠΌΠΈ ΠΌΠ°Ρ‚Ρ€ΠΈΡ†Π°ΠΌΠΈ для ΠΏΠΎΠ²Ρ‹ΡˆΠ΅Π½ΠΈΡ эффСктивности распараллСливания.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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