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An interval arithmetic domain decomposition method for a class of elliptic PDEs on nonrectangular domains

Hartmut Schwandt
1994 Journal of Computational and Applied Mathematics  
We introduce an interval arithmetic domain decomposition method for linear systems with interval coefficients resulting from the application of difference methods for a class of elliptic boundary value  ...  problems on domains with irregular geometry.  ...  interval version of stabilized block cyclic reduction ("interval Buneman") IBU, can be used [10, 12, 13] .  ... 
doi:10.1016/0377-0427(94)90324-7 fatcat:jtcj7wpr6nbjjou2hcchjf4xqa

Page 5340 of Mathematical Reviews Vol. , Issue 90I [page]

1990 Mathematical Reviews  
The interval arithmetic block-cyclic reduction is a direct method for solving systems of linear interval equations where the coefficient matrix has a special tridiagonal form.  ...  {Truncated interval-arithmetic block-cyclic reduction] Proceedings of the Annual Scientific Meeting of the GAMM (Vienna, 1988). Z. Angew. Math. Mech. 69 (1989), no. 4, T191-T193.  ... 

Basket Option Pricing Using GP-GPU Hardware Acceleration

Craig C. Douglas, Hyoseop Lee
2010 2010 Ninth International Symposium on Distributed Computing and Applications to Business, Engineering and Science  
We discretized the problem based on the alternating direction implicit (ADI) method and parallel cyclic reduction is applied to solve the set of tridiagonal matrices generated by the ADI method.  ...  To reduce the computational time of the problem, a general purpose graphics processing units (GP-GPU) environment is considered.  ...  Although the parallel cyclic reduction needs more arithmetic than cyclic reduction, there is an advantage in that parallel cyclic reduction uses more computing cores quite efficiently.  ... 
doi:10.1109/dcabes.2010.16 fatcat:xtikt55khraythwzaon4lfonxa

Nonlinear matrix equations and structured linear algebra

Beatrice Meini
2006 Linear Algebra and its Applications  
Relying on this scheme, the nth step of cyclic reduction can be performed in O(m 3 d n + m 2 d n log d n ) arithmetic operations; moreover, due to the quadratic convergence of cyclic reduction and to the  ...  Therefore one expects that the computational cost of cyclic reduction is much smaller than the computational cost of the doubling algorithm.  ...  Moreover, Algorithms based on the above result are presented in [30] but even for moderately large values of p > 2 they have shown numerical instability problems.  ... 
doi:10.1016/j.laa.2005.06.011 fatcat:nn36fsoz4zdixlnhpd7eedndka

GPU acceleration of Newton's method for large systems of polynomial equations in double double and quad double arithmetic [article]

Jan Verschelde, Xiangcheng Yu
2014 arXiv   pre-print
For double arithmetic, the evaluation and differentiation problem is memory bound, whereas for complex quad double arithmetic the problem is compute bound.  ...  The focus on this paper is on Newton's method, which requires the evaluation of the polynomials, their derivatives, and the solution of a linear system to compute the update to the current approximation  ...  The pivot block computes the actual components of the solution, while the other blocks compute the reductions for components at the low indices and write the reductions of the right hand side vector into  ... 
arXiv:1402.2626v2 fatcat:laj3n4hu3jactm35rzb3ygzz3e

A Parallel Fast Direct Solver for Block Tridiagonal Systems with Separable Matrices of Arbitrary Dimension

Tuomo Rossi, Jari Toivanen
1999 SIAM Journal on Scientific Computing  
The Divide & Conquer method has the arithmetical complexity O(N log N), and it is closely related to the cyclic reduction, but instead of using the matrix polynomial factorization the so{called partial  ...  A parallel fast direct solver based on the Divide & Conquer method for linear systems with separable block tridiagonal matrices is considered.  ...  The numerical experiments were carried out on a Cray T3E computer, located in Center for Scienti c Computing, Espoo, Finland.  ... 
doi:10.1137/s1064827597317016 fatcat:egagp2nbtvdm7m76opihilmuue

Polynomial circuit models for component matching in high-level synthesis

J. Smith, G. De Micheli
2001 IEEE Transactions on Very Large Scale Integration (vlsi) Systems  
Polynomials can be used to represent circuits that are described at the bit level or arithmetically.  ...  Design reuse requires engineers to determine whether or not an existing block implements desired functionality.  ...  Since both computations converged, but converged to different values, there is a discontinuity on the interval boundary.  ... 
doi:10.1109/92.974892 fatcat:br37ddwxhrccha5lpzhexbzzyy

Accelerating Iterative SpMV for the Discrete Logarithm Problem Using GPUs [chapter]

Hamza Jeljeli
2015 Lecture Notes in Computer Science  
This central operation can be accelerated on GPUs using specific computing models and addressing patterns, which increase the arithmetic intensity while reducing irregular memory accesses.  ...  In the context of cryptanalysis, computing discrete logarithms in large cyclic groups using index-calculus-based methods, such as the number field sieve or the function field sieve, requires solving large  ...  given cyclic group [16] .  ... 
doi:10.1007/978-3-319-16277-5_2 fatcat:442ccuiv2baqhjkfqsygdc67pm

Accelerating Iterative SpMV for Discrete Logarithm Problem Using GPUs [article]

Hamza Jeljeli
2014 arXiv   pre-print
This central operation can be accelerated on GPUs using specific computing models and addressing patterns, which increase the arithmetic intensity while reducing irregular memory accesses.  ...  In the context of cryptanalysis, computing discrete logarithms in large cyclic groups using index-calculus-based methods, such as the number field sieve or the function field sieve, requires solving large  ...  given cyclic group [16] .  ... 
arXiv:1209.5520v4 fatcat:yucl3rzthfarxlbfxuhwz4tcdm

The acceleration of matrix power methods by cyclic variations of the shift parameter

I.J.D. Craig, A.D. Sneyd
1989 Computers and Mathematics with Applications  
Indeed the cyclic shift technique works most effectively on those problems which are most recalcitrant to the traditional power method.  ...  We also apply the technique to accelerating the simultaneous determination of several dominant eigenmodes by the block power method.  ...  The computations were performed using 16 decimal digit arithmetic, and a Rayleigh quotient was taken for the eigenvalue.  ... 
doi:10.1016/0898-1221(89)90045-x fatcat:akpasjnscfd2tgnjozqhdnaini

Accelerated Iterative Methods for the Solution of Tridiagonal Systems on Parallel Computers

D. E. Heller, D. K. Stevenson, J. F. Traub
1976 Journal of the ACM  
Numerical experiments suggest that on a parallel computer this new algorithm is the best of the iterative algorithms we consider. (3.5) * = max|4a b | = 4||a A R ||. j J J We assume throughout that A >  ...  The theory has a natural extension to block tridiagonal systems.  ...  For systems such as Ml with n = 1000, APG is much better than cyclic reduction, requiring (on the STAR) 33,000 cycles versus 40,000 for Chebyshev and 69,000 for cyclic reduction.  ... 
doi:10.1145/321978.321983 fatcat:pltya2fqyffyhgrr6gq3vzdnhu

ENHANCED MAC ALGORITHM BASED ON THE USE OF MODULAR TRANSFORMATIONS

O. G. Korol
2014 Radìoelektronika, Ìnformatika, Upravlìnnâ  
-2 orders of known schemes based on block symmetric ciphers.  ...  of modular transformations, computational complexity reduce algorithm of the hashing schemes implementation using cyclic functions.  ...  For schemes on modular arithmetic the equivalent length of the key block symmetric cryptographic algorithm is shown (see. Table 2 ).  ... 
doi:10.15588/1607-3274-2015-1-8 fatcat:qwetg4a4u5dfzeqs75dwrptf5y

1. Solution of Partial Differential Equations on Vector and Parallel Computers [chapter]

1985 Solution of Partial Differential Equations on Vector and Parallel Computers  
The final algorithm is similar to the block cyclic reduction ones described above.  ...  One way to treat these problems is to view them as block tridiagonal and apply block cyclic reduction as 3.33 discussed in Lambiotte [1975] and Heller [1976] .  ...  "Fast Orthogonal Derivatives on the STAR," Comput. Math. Appl. 8, pp. 367-377. Boley, D. [1978] . "Vectorization of Block Relaxation Techniques: Some Numerical Experiments."  ... 
doi:10.1137/1.9781611971774.ch1 fatcat:zrhift3l2fhcjmvgscv3yf7wwi

Solving the Symmetric Tridiagonal Eigenvalue Problem on the Hypercube

Ilse C. F. Ipsen, Elizabeth R. Jessup
1990 SIAM Journal on Scientific and Statistical Computing  
This interval is reduced further with the computation of each eigenvalue. This continuous reduction of the initial search area is not possible when computing cyclically distributed eigenvalues.  ...  The regularity of the block (or the following cyclic) distribution scheme is lost. 3. Cyclic Distribution.  ... 
doi:10.1137/0911013 fatcat:kmgcvcvcefcpdolq7ylq6dpd4a

Page 2523 of Mathematical Reviews Vol. , Issue 98D [page]

1998 Mathematical Reviews  
(BG-RTU-CM; Ruse) On the stability of the cyclic reduction without back substitution for tridiagonal systems. (English summary) BIT 35 (1995), no. 3, 428-447.  ...  The main object under study is the interval linear system Ax = b with an interval n xn matrix A and an interval right-hand side m-vector b.  ... 
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