A floating-point technique for extending the available precision
From MaRDI portal
Publication:2549229
DOI10.1007/BF01397083zbMath0226.65034MaRDI QIDQ2549229
Publication date: 1971
Published in: Numerische Mathematik (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/132105
Related Items
Highly accurate verified error bounds for Krylov type linear system solvers, Precise evaluation of a polynomial at a point given in staggered correction format, Generation of test matrices with specified eigenvalues using floating-point arithmetic, Exact calculation of the overlap volume of spheres and mesh elements, Schur aggregation for linear systems and determinants, Algorithms for accurate, validated and fast polynomial evaluation, Adaptive and efficient algorithm for 2D orientation problem, Inversion of extremely ill-conditioned matrices in floating-point, Compensated summation and dot product algorithms for floating-point vectors on parallel architectures: error bounds, implementation and application in the Krylov subspace methods, Formalization of Double-Word Arithmetic, and Comments on “Tight and Rigorous Error Bounds for Basic Building Blocks of Double-Word Arithmetic”, Floating-point arithmetic on the test bench. How are verified numerical solutions calculated?, A method of obtaining verified solutions for linear systems suited for Java, Obtaining identical results with double precision global accuracy on different numbers of processors in parallel particle Monte Carlo simulations, The Schur aggregation and solving ill conditioned linear systems: the convergence theorem, Accurate evaluation of a polynomial and its derivative in Bernstein form, On a compensated Ehrlich-Aberth method for the accurate computation of all polynomial roots, Computation of the unit in the first place (ufp) and the unit in the last place (ulp) in precision-\(p\) base \(\beta\), Master-field simulations of \(\mathrm{O}(a)\)-improved lattice QCD: algorithms, stability and exactness, Forward stable eigenvalue decomposition of rank-one modifications of diagonal matrices, Floating-point arithmetic, Error bounds on complex floating-point multiplication with an FMA, Fast and accurate computation of the Euclidean norm of a vector, A regularization method for constrained nonlinear least squares, Additive preconditioning and aggregation in matrix computations, On relative errors of floating-point operations: Optimal bounds and applications, Development of a Stokes flow solver robust to large viscosity jumps using a Schur complement approach with mixed precision arithmetic, Formal verification of numerical programs: from C annotated programs to mechanical proofs, Some issues related to double rounding, Accurate evaluation algorithm for bivariate polynomial in Bernstein-Bézier form, High-precision computation: mathematical physics and dynamics, More accuracy at fixed precision., On design and implementation of a generic number type for real algebraic number computations based on expression dags, Error-free transformations of matrix multiplication by using fast routines of matrix multiplication and its applications, GPU-accelerated boundary element method for Helmholtz' equation in three dimensions, Primitive Floats in Coq, Accurate, validated and fast evaluation of elementary symmetric functions and its application, Accurate quotient-difference algorithm: error analysis, improvements and applications, A new subtraction-free formula for lower bounds of the minimal singular value of an upper bidiagonal matrix, The effects of rounding errors in the nodes on barycentric interpolation, Accurate and efficient evaluation of Chebyshev tensor product surface, Fast and accurate algorithm for the generalized exponential integral \(E_{\nu}(x)\) for positive real order, Accurate polynomial root-finding methods for symmetric tridiagonal matrix eigenproblems, Compensated de Casteljau algorithm in \(K\) times the working precision, TWO APPROXIMATE MINKOWSKI SUM ALGORITHMS, Accurate evaluation of a polynomial in Chebyshev form, Evading the drift in floating-point addition, Quantum Monte Carlo on graphical processing units, Accurate summation, dot product and polynomial evaluation in complex floating point arithmetic, Taylor models and floating-point arithmetic: proof that arithmetic operations are validated in COSY, Computing prime harmonic sums, Performance and accuracy of hardware-oriented native-, emulated- and mixed-precision solvers in FEM simulations, Fast and correctly rounded logarithms in double-precision, Efficiency of Reproducible Level 1 BLAS, Accurate simple zeros of polynomials in floating point arithmetic, Backward error analysis of the extended iterative refinement or improvement algorithm for solving ill conditioned linear system, Unnamed Item, Numerical validation of compensated summation algorithms with stochastic arithmetic, Performance and energy consumption of accurate and mixed-precision linear algebra kernels on GPUs, Selected Implementation Issues in Computation of the Grünwald-Letnikov Fractional-Order Difference by Means of Embedded System, Efficient Calculations of Faithfully Rounded l 2 -Norms of n -Vectors, A new error-free floating-point summation algorithm, Numerical validation of compensated algorithms with stochastic arithmetic, A fast parallel high-precision summation algorithm based on AccSumK, A note on Dekker's FastTwoSum algorithm, Development and acceleration of multiple precision arithmetic toolbox MuPAT for Scilab, An accurate algorithm for evaluating rational functions, Accurate evaluation of polynomials in Legendre basis, PACF: a precision-adjustable computational framework for solving singular values, SIMD Parallel Sparse Matrix-Vector and Transposed-Matrix-Vector Multiplication in DD Precision, \textsf{ORTHOPOLY}: a library for accurate evaluation of series of classical orthogonal polynomials and their derivatives, Rigorous integration of non-linear ordinary differential equations in Chebyshev basis, Improvement of error-free splitting for accurate matrix multiplication, Analysis of some known methods of improving the accuracy of floating-point sums, Verified compilation of floating-point computations, Algorithm 960, A generalized Kahan-Babuška-summation-algorithm
Uses Software
Cites Work
