Found 727 Documents (Results 1–100)
Rounding-error analysis of multigrid \(V\)-cycles. (English) Zbl 07931240
MSC:
65G50
Bounds on nonlinear errors for variance computation with stochastic rounding. (English) Zbl 07906817
MSC:
62-XX
Quadrature of functions with endpoint singular and generalised polynomial behaviour in computational physics. (English) Zbl 1537.65021
Adaptive precision sparse matrix-vector product and its application to Krylov solvers. (English) Zbl 1534.65070
Reviewer: Steven B. Damelin (Ann Arbor)
Formally-verified round-off error analysis of Runge-Kutta methods. (English) Zbl 07800194
MSC:
68V15
IEEE-754 precision-\(p\) base-\(\beta\) arithmetic implemented in binary. (English) Zbl 07912530
MSC:
65-XX
Combining sparse approximate factorizations with mixed-precision iterative refinement. (English) Zbl 07908566
MSC:
65-XX
Accurate calculation of Euclidean norms using double-word arithmetic. (English) Zbl 07908563
MSC:
65-XX
Numerical stability of algorithms at extreme scale and low precisions. (English) Zbl 1535.65060
Beliaev, Dmitry (ed.) et al., International congress of mathematicians 2022, ICM 2022, Helsinki, Finland, virtual, July 6–14, 2022. Volume 7. Sections 15–20. Berlin: European Mathematical Society (EMS). 5098-5117 (2023).
Model checking linear dynamical systems under floating-point rounding. (English) Zbl 1543.68222
Sankaranarayanan, Sriram (ed.) et al., Tools and algorithms for the construction and analysis of systems. 29th international conference, TACAS 2023, held as part of the European joint conferences on theory and practice of software, ETAPS 2023, Paris, France, April 22–27, 2023. Proceedings. Part I. Cham: Springer. Lect. Notes Comput. Sci. 13993, 47-65 (2023).
Precision-aware deterministic and probabilistic error bounds for floating point summation. (English) Zbl 1527.65030
MSC:
65G50
General framework for deriving reproducible Krylov subspace algorithms: BiCGStab case. (English) Zbl 1533.65049
Wyrzykowski, Roman (ed.) et al., Parallel processing and applied mathematics. 14th international conference, PPAM 2022, Gdansk, Poland, September 11–14, 2022. Revised selected papers. Part I. Cham: Springer. Lect. Notes Comput. Sci. 13826, 16-29 (2023).
Mixed precision low-rank approximations and their application to block low-rank LU factorization. (English) Zbl 1525.65038
Effects of round-to-nearest and stochastic rounding in the numerical solution of the heat equation in low precision. (English) Zbl 07726036
MSC:
65-XX
Computation of the unit in the first place (ufp) and the unit in the last place (ulp) in precision-\(p\) base \(\beta\). (English) Zbl 07681417
MSC:
65G99
Matrix multiplication in multiword arithmetic: error analysis and application to GPU tensor cores. (English) Zbl 1511.65040
Algorithm 1029: encapsulated error, a direct approach to evaluate floating-point accuracy. (English) Zbl 07908562
MSC:
65-XX
ABS: a formally correct software tool for space-efficient symbolic synthesis. (English) Zbl 07807727
Proceedings of the 25th ACM international conference on hybrid systems: computation and control, HSCC 2022, part of CPS-IoT week, Milan, Italy and virtual, May 4–6, 2022. New York, NY: Association for Computing Machinery (ACM). Paper No. 19, 10 p. (2022).
Formal verification of transcendental fixed- and floating-point algorithms using an automatic theorem prover. (English) Zbl 1522.68306
Symmetric transrationals: the data type and the algorithmic degree of its equational theory. (English) Zbl 1524.68199
Jansen, Nils (ed.) et al., A journey from process algebra via timed automata to model learning. Essays dedicated to Frits Vaandrager on the occasion of his 60th birthday. Cham: Springer. Lect. Notes Comput. Sci. 13560, 63-80 (2022).
MSC:
68Q65
On the possibility of increasing the accuracy of computations in the floating-point format with multiple exponents. (English) Zbl 07705584
Tchernykh, Andrei (ed.) et al., Mathematics and its applications in new computer systems. MANCS-2021. Proceedings of the international conference, Stavropol, Russia, December 13–15, 2021. Cham: Springer. Lect. Notes Netw. Syst. 424, 487-496 (2022).
MSC:
65-XX
Toward accurate and fast summation. (English) Zbl 07668772
MSC:
65-XX
A provably robust algorithm for triangle-triangle intersections in floating-point arithmetic. (English) Zbl 07666974
MSC:
65-XX
A novel and efficient square root computation quantum circuit for floating-point standard. (English) Zbl 1512.81025
Correct approximation of IEEE 754 floating-point arithmetic for program verification. (English) Zbl 1490.68078
Mixed-precision explicit stabilized Runge-Kutta methods for single- and multi-scale differential equations. (English) Zbl 07540376
An interval version of the Kuntzmann-Butcher method for solving the initial value problem. (English) Zbl 1499.65283
Solving block low-rank linear systems by LU factorization is numerically stable. (English) Zbl 1511.65024
Generation of test matrices with specified eigenvalues using floating-point arithmetic. (English) Zbl 1520.65030
Reviewer: Jan Mandel (Denver)
Formalization of double-word arithmetic, and comments on “Tight and rigorous error bounds for basic building blocks of double-word arithmetic”. (English) Zbl 07500134
MSC:
65-XX
Unrealistic models for realistic computations: how idealisations help represent mathematical structures and found scientific computing. (English) Zbl 1529.03073
Random number generators produce collisions: why, how many and more. (English) Zbl 07632878
MSC:
62-XX
Complexity and performance of secure floating-point polynomial evaluation protocols. (English) Zbl 1498.68050
Bertino, Elisa (ed.) et al., Computer security – ESORICS 2021. 26th European symposium on research in computer security, Darmstadt, Germany, October 4–8, 2021. Proceedings. Part II. Cham: Springer. Lect. Notes Comput. Sci. 12973, 352-369 (2021).
Exploiting verified neural networks via floating point numerical error. (English) Zbl 1497.68309
Drăgoi, Cezara (ed.) et al., Static analysis. 28th international symposium, SAS 2021, Chicago, IL, USA, October 17–19, 2021. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 12913, 191-205 (2021).
A computational status update for exact rational mixed integer programming. (English) Zbl 1482.90125
Singh, Mohit (ed.) et al., Integer programming and combinatorial optimization. 22nd international conference, IPCO 2021, Atlanta, GA, USA, May 19–21, 2021. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 12707, 163-177 (2021).
MSC:
90C11
Optimization modulo the theories of signed bit-vectors and floating-point numbers. (English) Zbl 1543.68349
Quantum image scaling based on bilinear interpolation with decimals scaling ratio. (English) Zbl 1528.81098
Deductive verification of floating-point Java programs in KeY. (English) Zbl 1474.68186
Groote, Jan Friso (ed.) et al., Tools and algorithms for the construction and analysis of systems. 27th international conference, TACAS 2021, held as part of the European joint conferences on theory and practice of software, ETAPS 2021, Luxembourg City, Luxembourg, March 27 – April 1, 2021. Proceedings. Part II. Cham: Springer. Lect. Notes Comput. Sci. 12652, 242-261 (2021).
Error bounds for the numerical evaluation of Legendre polynomials by a three-term recurrence. (English) Zbl 1464.65021
Stochastic rounding and its probabilistic backward error analysis. (English) Zbl 1462.65050
MSC:
65G50
Solution to the main problem of the artificial satellite by reverse normalization. (English) Zbl 1516.70042
A generalized floating-point quantum representation of 2-D data and their applications. (English) Zbl 1509.81318
MSC:
81P68
On the use of the infinity computer architecture to set up a dynamic precision floating-point arithmetic. (English) Zbl 1491.65179
MSC:
65Y04
Error analysis and improving the accuracy of Winograd convolution for deep neural networks. (English) Zbl 1486.65285
Counterexample- and simulation-guided floating-point loop invariant synthesis. (English) Zbl 1474.68055
Pichardie, David (ed.) et al., Static analysis. 27th international symposium, SAS 2020, virtual event, November 18–20, 2020. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 12389, 156-177 (2020).
Numerical algorithms for high-performance computational science. (English) Zbl 1462.65231
Philos. Trans. R. Soc. Lond., A, Math. Phys. Eng. Sci. 378, No. 2166, Article ID 20190066, 18 p. (2020).
MSC:
65Y10
Analysis of the stability of periodic linear difference equation systems on extended floating-point numbers. (English) Zbl 1465.39006
CHIMERA: combining ring-LWE-based fully homomorphic encryption schemes. (English) Zbl 1462.94030
MSC:
94A60
Evaluation of Legendre polynomials by a three-term recurrence in floating-point arithmetic. (English) Zbl 1466.65226
Efficiency and accuracy improvements of secure floating-point addition over secret sharing. (English) Zbl 1471.68093
Aoki, Kazumaro (ed.) et al., Advances in information and computer security. 15th international workshop on security, IWSEC 2020, Fukui, Japan, September 2–4, 2020. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 12231, 77-94 (2020).
A reliable algorithm to check the accuracy of iterative schemes for solving nonlinear equations: an application of the CESTAC method. (English) Zbl 1456.65032
Error analysis of some operations involved in the Cooley-Tukey fast Fourier transform. (English) Zbl 1484.65348
Non-replicability circumstances in a neural network model with Hodgkin-Huxley-type neurons. (English) Zbl 1451.92012
Sharper probabilistic backward error analysis for basic linear algebra kernels with random data. (English) Zbl 1452.65090
Stability analysis of inline ZFP compression for floating-point data in iterative methods. (English) Zbl 1453.65096
Control of accuracy of Taylor-collocation method to solve the weakly regular Volterra integral equations of the first kind by using the CESTAC method. (English) Zbl 1463.65432
Cause and origin of Moire interferences in recursive processes and with fixed-point and floating-point data types. (English) Zbl 1470.65038
Optimizing secure floating-point arithmetic: sums, dot products, and polynomials. (English) Zbl 1463.94034
A dynamic precision floating-point arithmetic based on the Infinity Computer framework. (English) Zbl 07250760
Sergeyev, Yaroslav D. (ed.) et al., Numerical computations: theory and algorithms. Third international conference, NUMTA 2019, Crotone, Italy, June 15–21, 2019. Revised selected papers. Part II. Cham: Springer. Lect. Notes Comput. Sci. 11974, 289-297 (2020).
MSC:
65-XX
Mixed precision block fused multiply-add: error analysis and application to GPU tensor cores. (English) Zbl 1452.65425
Interval methods of Adams-Bashforth type with variable step sizes. (English) Zbl 07202185
MSC:
65-XX
A generalized floating-point representation and manipulation of quantum signals based on IEEE-754. (English) Zbl 1440.81027
Higher-order and higher floating-point precision numerical approximations of finite strain elasticity moduli. (English) Zbl 07841260
An efficient parametric linear programming solver and application to polyhedral projection. (English) Zbl 1539.68188
Chang, Bor-Yuh Evan (ed.), Static analysis. 26th international symposium, SAS 2019, Porto, Portugal, October 8–11, 2019. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 11822, 203-224 (2019).
Neural network precision tuning. (English) Zbl 1537.68038
Parker, David (ed.) et al., Quantitative evaluation of systems. 16th international conference, QEST 2019, Glasgow, UK, September 10–12, 2019. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 11785, 129-143 (2019).
Icing: supporting fast-math style optimizations in a verified compiler. (English) Zbl 1533.68034
Dillig, Isil (ed.) et al., Computer aided verification. 31st international conference, CAV 2019, New York City, NY, USA, July 15–18, 2019. Proceedings. Part II. Cham: Springer. Lect. Notes Comput. Sci. 11562, 155-173 (2019).
Eliminating unstable tests in floating-point programs. (English) Zbl 1524.68104
Mesnard, Fred (ed.) et al., Logic-based program synthesis and transformation. 28th international symposium, LOPSTR 2018, Frankfurt/Main, Germany, September 4–6, 2018. Revised selected papers. Cham: Springer. Lect. Notes Comput. Sci. 11408, 169-183 (2019).
Primitive floats in Coq. (English) Zbl 07649956
Harrison, John (ed.) et al., 10th international conference on interactive theorem proving, ITP 2019, September 9–12, 2019, Portland, OR, USA. Proceedings. Wadern: Schloss Dagstuhl – Leibniz-Zentrum für Informatik. LIPIcs – Leibniz Int. Proc. Inform. 141, Article 7, 20 p. (2019).
MSC:
68V15
Identifying volatile numeric expressions in numeric computing applications. (English) Zbl 1540.68054
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