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

1994
*
Journal of Computational and Applied Mathematics
*

We introduce an

doi:10.1016/0377-0427(94)90324-7
fatcat:jtcj7wpr6nbjjou2hcchjf4xqa
*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] . ...##
###
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. ...##
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Basket Option Pricing Using GP-GPU Hardware Acceleration

2010
*
2010 Ninth International Symposium on Distributed Computing and Applications to Business, Engineering and Science
*

We discretized the problem based

doi:10.1109/dcabes.2010.16
fatcat:xtikt55khraythwzaon4lfonxa
*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. ...##
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Nonlinear matrix equations and structured linear algebra

2006
*
Linear Algebra and its Applications
*

Relying

doi:10.1016/j.laa.2005.06.011
fatcat:nn36fsoz4zdixlnhpd7eedndka
*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. ...##
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GPU acceleration of Newton's method for large systems of polynomial equations in double double and quad double arithmetic
[article]

2014
*
arXiv
*
pre-print

For double

arXiv:1402.2626v2
fatcat:laj3n4hu3jactm35rzb3ygzz3e
*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 ...##
###
A Parallel Fast Direct Solver for Block Tridiagonal Systems with Separable Matrices of Arbitrary Dimension

1999
*
SIAM Journal on Scientific Computing
*

The Divide & Conquer method has the

doi:10.1137/s1064827597317016
fatcat:egagp2nbtvdm7m76opihilmuue
*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. ...##
###
Polynomial circuit models for component matching in high-level synthesis

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

doi:10.1109/92.974892
fatcat:br37ddwxhrccha5lpzhexbzzyy
*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. ...##
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Accelerating Iterative SpMV for the Discrete Logarithm Problem Using GPUs
[chapter]

2015
*
Lecture Notes in Computer Science
*

This central operation can be accelerated

doi:10.1007/978-3-319-16277-5_2
fatcat:442ccuiv2baqhjkfqsygdc67pm
*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] . ...##
###
Accelerating Iterative SpMV for Discrete Logarithm Problem Using GPUs
[article]

2014
*
arXiv
*
pre-print

This central operation can be accelerated

arXiv:1209.5520v4
fatcat:yucl3rzthfarxlbfxuhwz4tcdm
*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] . ...##
###
The acceleration of matrix power methods by cyclic variations of the shift parameter

1989
*
Computers and Mathematics with Applications
*

Indeed the

doi:10.1016/0898-1221(89)90045-x
fatcat:akpasjnscfd2tgnjozqhdnaini
*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. ...##
###
Accelerated Iterative Methods for the Solution of Tridiagonal Systems on Parallel Computers

1976
*
Journal of the ACM
*

Numerical experiments suggest that

doi:10.1145/321978.321983
fatcat:pltya2fqyffyhgrr6gq3vzdnhu
*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*. ...##
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ENHANCED MAC ALGORITHM BASED ON THE USE OF MODULAR TRANSFORMATIONS

2014
*
Radìoelektronika, Ìnformatika, Upravlìnnâ
*

-2 orders of known schemes based

doi:10.15588/1607-3274-2015-1-8
fatcat:qwetg4a4u5dfzeqs75dwrptf5y
*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 ). ...##
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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

doi:10.1137/1.9781611971774.ch1
fatcat:zrhift3l2fhcjmvgscv3yf7wwi
*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." ...##
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Solving the Symmetric Tridiagonal Eigenvalue Problem on the Hypercube

1990
*
SIAM Journal on Scientific and Statistical Computing
*

This

doi:10.1137/0911013
fatcat:kmgcvcvcefcpdolq7ylq6dpd4a
*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. ...##
###
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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