A parallel algorithm for calculation of determinants and minors using arbitrary precision arithmetic

DOI10.1007/s10543-015-0547-zzbMath1338.65117arXiv1308.1536OpenAlexW1984863950MaRDI QIDQ285264

Gleb Beliakov, Yu. V. Matiyasevich

Publication date: 19 May 2016

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1308.1536

zbMATH Keywords

numerical exampleparallel algorithmsill-conditioned matrixdeterminantmessage passing interfaceGPURiemann's zeta function

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Computation of special functions and constants, construction of tables (65D20) Parallel numerical computation (65Y05) Numerical computation of determinants (65F40)

Related Items (6)

Balanced incomplete factorization preconditioner with pivoting ⋮ A New Analysis of Iterative Refinement and Its Application to Accurate Solution of Ill-Conditioned Sparse Linear Systems ⋮ A review note on arbitrary precision arithmetic ⋮ COMPUTATION OF A DETERMINANT AND A MATRIX PRODUCT IN CELLULAR AUTOMATA ⋮ Riemann’s zeta function and finite Dirichlet series ⋮ Plausible ways for calculating the Riemann zeta function via the Riemann-Siegel theta function

Uses Software

• gmp
• Mathemagix
• MPFI
• ScaLAPACK
• MPFR
• SUMMA
• CALU
• Elemental
• Arb
• MAGMA
• PLASMA
• MPIGMP
• GPUprec
• CUMP

Cites Work

• Unnamed Item
• The Riemann hypothesis. A resource for the afficionado and virtuoso alike
• Matrix multiplication via arithmetic progressions
• Gaussian elimination is not optimal
• Fast multiplication of large numbers
• Communication-optimal Parallel and Sequential QR and LU Factorizations
• Minimizing Communication in Numerical Linear Algebra
• Modular SIMD arithmetic in M <scp>athemagix</scp>
• Elemental
• CALU: A Communication Optimal LU Factorization Algorithm
• MPFR
• ScaLAPACK Users' Guide
• Approximation of Riemann’s Zeta Function by Finite Dirichlet Series: A Multiprecision Numerical Approach
• Proof of existence of global solutions form-component reaction–diffusion systems with mixed boundary conditions via the Lyapunov functional method

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