by Pavel Holoborodko on January 13, 2021

Recent papers citing the toolbox (*updating*):

- Craciunescu, T., Murari, A.,
*Detecting causal relations in time series with the new cross Markov Matrix technique*, Nonlinear Dynamics (2021), January 13, 2020. - Hong Chen, Ee Hou Yong,
*Reconstructing Stieltjes functions from their approximate values: a search for a needle in a hay stack*, arXiv:2101.03828, January 12, 2020. - Breton, L., González-Casanova, P. & Montoya, C.,
*RBF collocation and hybrid-LHI methods for Stokes systems and its application to controllability problems*, Computational and Applied Mathematics 40-15 (2021), January 8, 2021. - Yury Grabovsky,
*Reconstructing Stieltjes functions from their approximate values: a search for a needle in a hay stack*, arXiv:2101.02775, January 7, 2020. - Rick Hubertus Sijbrandus Budé and Dirk Van Eester and Jan van Dijk and Roger J E Jaspers and A. B. Smolders,
*Accelerating simulations of electromagnetic waves in hot, magnetized fusion plasmas*, Plasma Physics and Controlled Fusion, December 22, 2020. - Gengyu Xu, George V. Eleftheriades, and Sean V. Hum,
*Approach to the analysis and synthesis of cylindrical metasurfaces with noncircular cross sections based on conformal transformations*, Physical Review B 102, December 22, 2020. - Bucha, B., Kuhn, M. A,
*A numerical study on the integration radius separating convergent and divergent spherical harmonic series of topography-implied gravity*, Journal of Geodesy, 94, November 2020. - Reuben Rauch, Manfred R.Trummer, J.F.Williams,
*A spectral collocation method for mixed functional differential equations*, Applied Numerical Mathematics Volume 161, March 2021, Pages 101-110. - F.Fantoni, L.Morini, A.Bacigalupo, M.Paggi,
*The generalized Floquet-Bloch spectrum for periodic thermodiffusive layered materials*, International Journal of Mechanical Sciences, November 5, 2020. - H. Betar, D. Del Sarto, M. Ottaviani and A. Ghizzo,
*Multiparametric study of tearing modes in thin current sheets*, Physics of Plasmas 27, October 14, 2020. - Pavel M. Lushnikov, Denis A. Silantyev, Michael Siegel,
*Collapse vs. blow up and global existence in the generalized Constantin-Lax-Majda equation*, arXiv:2010.01201, October 2, 2020.

Previous issues: digest v.16, digest v.15, digest v.14, digest v.13, digest v.12, digest v.11, digest v.10, digest v.9, digest v.8, digest v.7, digest v.6, digest v.5, digest v.4, digest v.3 and digest v.2.

by Pavel Holoborodko on October 9, 2020

Recent papers citing the toolbox:

- Bengt Fornberg,
*Euler–Maclaurin expansions without analytic derivatives*, University of Colorado, September 30, 2020. - Hongbin Chen, Changtao Sheng, Li-Lian Wang,
*On explicit form of the FEM stiffness matrix for the integral fractional Laplacian on non-uniform meshes*, arXiv:2009.04886, September 10, 2020. - Xiangming Xiong, Jianjun Tao,
*Linear stability and energy stability of plane Poiseuille flow with isotropic and anisotropic slip boundary conditions*, Physics of Fluids, Volume 32, Issue 9, September 8, 2020. - Nicholas Higham and Xiaobo Liu,
*A Multiprecision Derivative-Free Schur–Parlett Algorithm for Computing Matrix Functions*, MIMS Preprint, September 7, 2020. - Richard S. Falk, Roger D. Nussbaum,
*Hidden Positivity and a New Approach to Numerical Computation of Hausdorff Dimension: Higher Order Methods*, arXiv:2008.11150, August 25, 2020. - Natalie Klco, Martin J. Savage,
*Geometric Quantum Information Structure in Quantum Fields and their Lattice Simulation*, arXiv:2008.03647, August 9, 2020. - Ilya Tyuryukanov, Marjan Popov,
*D-Decomposition Based Robust Discrete-Time Current Regulator for Grid-Connected VSI*, IEEE, July 30, 2020. - Bengt Fornberg,
*Generalizing the trapezoidal rule in the complex plane*, Numerical Algorithms, July 21, 2020. - Bengt Fornberg,
*Contour integrals of analytic functions given on a grid in the complex plane*, IMA Journal of Numerical Analysis, July 20, 2020. - Zeyu Liao, Ken Hayami, Keiichi Morikuni, Jun-Feng Yin,
*A Stabilized GMRES Method for Solving Underdetermined Least Squares Problems*, arXiv:2007.10853, July 19, 2020. - Rasmus Tamstorf, Joseph Benzaken, Stephen F. McCormick,
*Discretization-error-accurate mixed-precision multigrid solvers*, arXiv:2007.06628, July 13, 2020. - Mayeul Arminjon,
*An analytical model for the Maxwell radiation field in an axially symmetric galaxy*, July 2, 2020. - Yasuo Tsushima, Koji Hasegawa,
*Computing Group Velocities and Group-Velocity Dispersions of Optical Fibers Through Automatic Differentiation of Explicit Forms of Propagation Constants*, Journal of Lightwave Technology, Volume: 38, Issue: 21, June 24, 2020. - Elisabet Edvardsson, Flore K. Kunst, Tsuneya Yoshida, Emil J. Bergholtz,
*Phase Transitions and Generalized Biorthogonal Polarization in Non-Hermitian Systems*, arXiv:2006.12898, June 23, 2020. - Ning Cai, Xuewei Yang,
*A Computational Approach to First Passage Problems of Reflected Hyperexponential Jump Diffusion Processes*, June 22, 2020. - K.Maes, M.N.Chatzis, R.Vandebril, G.Lombaert,
*Observability of modally reduced order models with unknown parameters*, Mechanical Systems and Signal Processing, Volume 146, January 1, 2021. - Josephine Dufitinema, Seppo Pynnönen and Tommi Sottinen,
*Maximum likelihood estimators from discrete data modeled by mixed fractional Brownian motion with application to the Nordic stock markets*, Communications in Statistics – Simulation and Computation, May 30, 2020. - Massimiliano Fasi and Bruno Iannazzo,
*The dual inverse scaling and squaring algorithm for the matrix logarithm*, MIMS Preprint, May 27, 2020. - S.M. Rump,
*On recurrences converging to the wrong limit in finite precision and some new examples*, Electronic Transactions on Numerical Analysis (ETNA), 52:358–369, 2020. - Abhinav Dronamraju, Songyan Li, Qirui Li, Yuting Li, Daniel Tylavsky, Di Shi, Zhiwei Wang,
*Implications of Stahl’s Theorems to Holomorphic Embedding Pt. 2: Numerical Convergence*, arXiv:2003.07457, March 18, 2020. - Xihong Xu and Lifeng Li,
*Numerical instability of the C method when applied to coated gratings and methods to avoid it*, Journal of the Optical Society of America. A, Optics, Image Science, and Vision, April 1, 2020, 37(4):511-520. - Dylan Abrahamsen,
*Space-Time Evolution with Radial Basis Functions and Hermite-Based Finite Difference Methods*, University of Colorado at Boulder, 2020.

Previous issues: digest v.15, digest v.14, digest v.13, digest v.12, digest v.11, digest v.10, digest v.9, digest v.8, digest v.7, digest v.6, digest v.5, digest v.4, digest v.3 and digest v.2.

by Pavel Holoborodko on February 8, 2020

Recent papers citing the toolbox:

- (Book) Nathan Mendes, Marx Chhay, Julien Berger, Denys Dutykh,
*Numerical Methods for Diffusion Phenomena in Building Physics*, Springer, ISBN: 978-3-030-31573-3. - Nicholas Higham and Srikara Pranesh,
*Exploiting Lower Precision Arithmetic in Solving Symmetric Positive Definite Linear Systems and Least Squares Problems*, MIMS Preprint, November 6, 2019. - Nicholas Higham and Théo Mary,
*A New Approach to Probabilistic Rounding Error Analysis*, SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2019. - Nicholas Higham and Théo Mary,
* A New Preconditioner that Exploits Low-Rank Approximations
to Factorization Error*, SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2019. - Massimiliano Fasi,
*Computing matrix functions in arbitrary precision arithmetic*, PhD Thesis, August 1, 2019. - Takeshi Terao, Katsuhisa Ozaki, Takeshi Ogita,
*LU-Cholesky QR algorithms for thin QR decomposition*, Parallel Computing, Volume 92, April 2020. - Takeshi Ogita, Kensuke Aishima,
*Iterative refinement for singular value decomposition based on matrix multiplication*Journal of Computational and Applied Mathematics, Volume 369, 1 May 2020. - Abe C. Ellison, Bengt Fornberg,
*A parallel-in-time approach for wave-type PDEs*, arXiv:1907.11771, July 26, 2019. - Grady B. Wright, Bengt Fornberg,
*Stable computations with flat radial basis functions using vector-valued rational approximations*J. Comput. Physics 331: 137-156 (2017) - Gnecco, G., Nutarelli, F.,
*On the trade-off between number of examples and precision of supervision in machine learning problems*Optimization Letters, September 30, 2019. - Ch. Tsitouras and Ioannis Th. Famelis,
*Extended precision rational L∞ approximations to the matrix exponential*AIP Conference Proceedings, 2019. - (Book)Edited By: A.H.-D. Cheng, University of Mississippi, USA; A. Tadeu, University of Coimbra
*Boundary Elements and other Mesh Reduction Methods XLII*ISBN: 978-1-78466-341-4. - Jorge Cayama and Carlota M. Cuesta and Francisco de la Hoz,
*Numerical Approximation of the Fractional Laplacian on R Using Orthogonal Families*, arXiv:2001.08825, January 23, 2020. - Qiang Xi, C.S.Chen, Zhuojia Fu, Eva Comino
*The MAPS with polynomial basis functions for solving axisymmetric time-fractional equations*, Computers & Mathematics with Applications, Elsevier, December 6, 2019. - E. G. Charalampidis, N. Boullé, P. E. Farrell, P. G. Kevrekidis,
*Bifurcation analysis of stationary solutions of two-dimensional coupled Gross-Pitaevskii equations using deflated continuation*, arXiv:1912.00023, November 29, 2019. - Yiran Xu, Jingye Li, Xiaohong Chen, Guofei Pang,
*Solving fractional Laplacian visco-acoustic wave equations on complex-geometry domains using Grünwald-formula based radial basis collocation method*, Computers & Mathematics with Applications, Elsevier, October 29, 2019. - Myeong-Seok Go, Jae Hyuk Lim, Jin-Gyun Kim, Ki-ryoung Hwang,
*A family of Craig–Bampton methods considering residual mode compensation*, Applied Mathematics and Computation
Volume 369, October 28, 2019. - Stepčenko Artūrs,
*Forecasting System Development for Nonlinear and Nonstationary Time Series of Normalized Difference Vegetation Index*, PhD Thesis. Rīga, October 16, 2019. - Fatih Kangal, Emre Mengi,
*Nonsmooth algorithms for minimizing the largest eigenvalue with applications to inner numerical radius*, IMA Journal of Numerical Analysis, November 13, 2019. - Tersoo Luga and Bernard Alechenu,
*Numerical Solutions of Some Second Order Partial Differential
Equations using Non-Standard Exponent Values of the
Generalized Multiquadric Radial Basis Function*, IOSR Journal of Mathematics, Volume 15, Issue 3, June 2019.

Previous issues: digest v.14, digest v.13, digest v.12, digest v.11, digest v.10, digest v.9, digest v.8, digest v.7, digest v.6, digest v.5, digest v.4, digest v.3 and digest v.2.

by Pavel Holoborodko on July 23, 2019

Recent papers citing the toolbox:

- B. Bucha, C. Hirt, M. Kuhn,
*Cap integration in spectral gravity forward modelling up to the full gravity tensor*, Journal of Geodesy, 2019, DOI: 10.1007/s00190-019-01277-3. - M. Berljafa, S. Elsworth, S. Güttel,
*Rational Krylov Toolbox for MATLAB 2.8*, February 25, 2019, Manchester University. - J. Wang, I. Tyuryukanov, A. Monti,
*Design of a novel robust current controller for grid-connected inverter against grid impedance variations*, International Journal of Electrical Power & Energy Systems, Volume 110, September 2019, Pages 454-466. - T. Luga, T. Aboiyar, S. Adee,
*Radial basis function methods for approximating the two-dimensional heat equation*, International Journal of Engineering Applied Sciences and Technology, 2019, Vol. 4, Issue 2, ISSN No. 2455-2143, Pages 7-15. - M. Fasi, B. Iannazzo,
*Substitution algorithms for rational matrix equations*, MIMS Preprint, May 12, 2019. - P. Maxwell, S. Ellingsen,
*Path-following methods for calculating linear surface wave dispersion relations on vertical shear flows*, arXiv:1905.03187, May 5, 2019. - Xi, Q., Fu, ZJ. & Rabczuk,
*An efficient boundary collocation scheme for transient thermal analysis in large-size-ratio functionally graded materials under heat source load*, Computational Mechanics, Springer Berlin, April 2019. - J. Cave,
*Modelling Novel Photovoltaic Devices*, PhD thesis, September 2018.

Previous issues: digest v.13, digest v.12, digest v.11, digest v.10, digest v.9, digest v.8, digest v.7, digest v.6, digest v.5, digest v.4, digest v.3 and digest v.2.

by Pavel Holoborodko on February 27, 2019

Recent papers citing the toolbox:

- J. Lehtonen, G. A. Parker,
*Evolution of the Two Sexes under Internal Fertilization and Alternative Evolutionary Pathways*, The American Naturalist, March 18, 2019. - T. Ogita, K. Aishima,
*Iterative refinement for symmetric eigenvalue decomposition II: clustered eigenvalues*, Japan Journal of Industrial and Applied Mathematics, February 22, 2019. - S. Elsworth, S. Güttel,
*The block rational Arnoldi method*,MIMS Preprint, February 17, 2019. - F. Mumtaz, H. Saidaoui, F.H. Alharbi,
*Efficient high order method for differential equations in unbounded domains using generalized coordinate transformation*, Journal of Computational Physics, Volume 381, 15 March 2019, Pages 275-289. - M.F. Rios, J. Calder, G. Lerman,
*Algorithms for -based semi-supervised learning on graphs*, arXiv:1901.05031, January 15, 2019. - Z.J. Fu, L.W. Yang, H.Q. Zhu, W.Z Xu,
*A semi-analytical collocation Trefftz scheme for solving multi-term time fractional diffusion-wave equations*, Engineering Analysis with Boundary Elements, Volume 98, January 2019, Pages 137-146. - M. Fasi, B. Iannazzo,
*Computing primary solutions of equations involving primary matrix functions*, Linear Algebra and its Applications, Volume 560, January 1, 2019, Pages 17-42.

Previous issues: digest v.12, digest v.11, digest v.10, digest v.9, digest v.8, digest v.7, digest v.6, digest v.5, digest v.4, digest v.3 and digest v.2.

by Pavel Holoborodko on September 24, 2018

Recent papers citing the toolbox:

- N. Higham, S. Pranesh, M. Zounon,
*Squeezing a Matrix into Half Precision, with an Application to Solving Linear Systems*, November 26, 2018. - N. Higham, M. Fasi,
*An Arbitrary Precision Scaling and Squaring Algorithm for the Matrix Exponential*, November 24, 2018. - A. Bacigalupo, M.L. De Bellis, G. Gnecco,
*Complex frequency band structure of periodic thermo-diffusive materials by Floquet-Bloch theory*, arXiv:1811.09389, November 23, 2018. - P.G. Casanova, L. Breton, C. Montoya,
*RBFs methods for null control problems of the Stokes system with Dirichlet and Navier slip boundary conditions*, arXiv:1811.00459, November 1, 2018. - J. Idígoras, L. Contreras‐Bernal, James M. Cave, Nicola E. Courtier, Á. B. Ana Borras, Juan R. Sánchez‐Valencia, Juan A. Anta, Alison B. Walker,
*The Role of Surface Recombination on the Performance of Perovskite Solar Cells: Effect of Morphology and Crystalline Phase of TiO2 Contact*, October 8, 2018. - T. Fukaya, R. Kannan, Y. Nakatsukasa, Y. Yamamoto, Y. Yanagisawa,
*Shifted CholeskyQR for computing the QR factorization of ill-conditioned matrices*, arXiv:1809.11085, September 28, 2018. - I. Evdokimova, J. Verdú, P. de Paco,
*Bandpass Phase Correction Methodology for Ladder-Type Acoustic Filters*, 48th European Microwave Conference (EuMC), September 23-27, 2018. - B. Fornberg, J.A. Reeger,
*An improved Gregory-like method for 1-D quadrature*, Numerische Mathematik, August 16, 2018. - J.M.Linares, G.Goch, A.Forbes, J.M.Sprauel, A.Clément, F.Haertige, W.Gao,
*Modelling and traceability for computationally-intensive precision engineering and metrology*, CIRP Annals, Volume 67, Issue 2, 2018, Pages 815-838. - M. Kalfa, Ö. Ergül, V.B. Ertürk,
*Error Control of Multiple-Precision MLFMA*, IEEE Transactions on Antennas and Propagation, July 9, 2018. - W. Tian, G. Rui, D. Dong, J. Kang,
*Efficient blind adaptive Karhunen–Loéve transform via parallel search*, International Journal of Distributed Sensor Networks, Volume 14, Issue 6, June 1, 2018. - D. Lu, D. Kressner, B. Vandereycken,
*Subspace acceleration for the Crawford number computation*. - S. Fodor, Z. Németh,
*Numerical analysis of parallel implementation of the reorthogonalized ABS methods*, Central European Journal of Operations Research, 2018. - Z.J. Fu, Q. Xi, W. Chen, A.H.D. Cheng,
*A boundary-type meshless solver for transient heat conduction analysis of slender functionally graded materials with exponential variations*, Computers & Mathematics with Applications, Volume 76, Issue 4, 15 August 2018, Pages 760-773. - M. E. Hochstenbach, C. Mehl, B. Plestenjak,
*Solving singular generalized eigenvalue problems by a rank-completing perturbation*, arXiv:1805.07657, May 19, 2018. - S. Bertoluzza, D. Prada,
*A Polygonal Discontinuous Galerkin Method with Minus One Stabilization*, arXiv:1805.04196, May 10, 2018.

Previous issues: digest v.11, digest v.10, digest v.9, digest v.8, digest v.7, digest v.6, digest v.5, digest v.4, digest v.3 and digest v.2.

by Pavel Holoborodko on April 12, 2018

Recent papers citing the toolbox:

- T. Ogita, K. Aishima,
*Iterative refinement for symmetric eigenvalue decomposition*, Japan Journal of Industrial and Applied Mathematics, May 11, 2018. - N. Higham, M. Theo,
*A New Preconditioner that Exploits Low-Rank Approximations to Factorization Error*, April 23, 2018. - M.J.Y. Ou, H.J. Woerdeman,
*On the augmented Biot-JKD equations with Pole-Residue representation of the dynamic tortuosity*, arXiv:1805.00335, April 28, 2018. - X. Shui, S. Wang,
*Closed-form numerical formulae for solutions of strongly nonlinear oscillators*, International Journal of Non-Linear Mechanics, Volume 103, July 2018, Pages 12–22. - B. Pan, Y. Wang, S. Tian,
*A High-Precision Single Shooting Method for Solving Hypersensitive Optimal Control Problems*, Mathematical Problems in Engineering, Volume 2018, April 15, 2018. - A. Doak, J.-M. Vanden-Broeck,
*Solution selection of axisymmetric Taylor bubbles*, Journal of Fluid Mechanics, Volume 843, May 25, 2018, pp. 518-535. - B. Bucha, C. Hirt, M. Kuhn,
*Cap integration in spectral gravity forward modelling: near- and far-zone gravity effects via Molodensky’s truncation coefficients*, Journal of Geodesy (2018), April 5, 2018. - R. Klees, D.C. Slobbe, H.H. Farahani,
*How to deal with the high condition number of the noise covariance matrix of gravity field functionals synthesised from a satellite-only global gravity field model?*, Journal of Geodesy (2018), March 23, 2018. - G. Li, L. Deng, G. Xiao, P. Tang, C. Wen, W. Hu, J. Pei, L. Shi, H. Eugene Stanley,
*Enabling Controlling Complex Networks with Local Topological Information*, Scientific Reports Volume 8, Article number: 4593 (2018), March 15, 2018. - W. Lin, Z. Wang, M. Huang, Y. Zhuang, S. Zhang,
*On structural identifiability analysis of the cascaded linear dynamic systems in isotopically non-stationary 13C labelling experiments*, Mathematical Biosciences, Volume 300, June 2018, pages 122-129. - M. Pollak, M. Shauly-Aharonov,
*A Double Recursion for Calculating Moments of the Truncated Normal Distribution and its Connection to Change Detection*, Methodology and Computing in Applied Probability (2018). - F. Mumtaz, F. Alharbi,
*Efficient Mapping of High Order Basis Sets for Unbounded Domains*, Commun. Comput. Phys., doi: 10.4208/cicp.OA-2017-0067. - N. E. Courtier, G. Richardson, J. M. Foster,
*A fast and robust numerical scheme for solving models of charge carrier transport and ion vacancy motion in perovskite solar cells*, arXiv:1801.05737, January 17, 2018. - K. Tanaka, M. Sugihara,
*Design of accurate formulas for approximating functions in weighted Hardy spaces by discrete energy minimization*, arXiv:1801.04363, January 13, 2018. - T. Plakhotnik, J. Reichardt,
*Relation between Raman backscattering from droplets and bulk water: Effect of refractive index dispersion*, arXiv:1712.08474, December 21, 2017. - N. Higham,
*A Multiprecision World*, SIAM news, Volume 50, Issue 8, October, 2017.

Previous issues: digest v.10, digest v.9, digest v.8, digest v.7, digest v.6, digest v.5, digest v.4, digest v.3 and digest v.2.

by Pavel Holoborodko on September 27, 2017

Recent papers citing the toolbox:

- E. D. Schiappacasse, C. J. Fewster, L. H. Ford,
*Vacuum Quantum Stress Tensor Fluctuations: A Diagonalization Approach*, arXiv:1711.09477, November 26, 2017. - B. Protas, T. Sakajo,
*Harnessing the Kelvin-Helmholtz Instability: Feedback Stabilization of an Inviscid Vortex Sheet*, arXiv:1711.03249, November 9, 2017. - Z. Chen, C. Hauck,
*Multiscale convergence properties for spectral approximations of a model kinetic equation*, arXiv:1710.05500, October 16, 2017. - D. Tayli, M. Capek, L. Akrou, V. Losenicky, L. Jelinek, M. Gustafsson,
*Accurate and Efficient Evaluation of Characteristic Modes*, arXiv:1709.09976, September 26, 2017. - E. Lehto, V. Shankar, G. Wright,
*A Radial Basis Function (RBF) Compact Finite Difference (FD) Scheme for Reaction-Diffusion Equations on Surfaces*, SIAM J. Sci. Comput., 39(5), A2129–A2151. - E. Onofri,
*Efficient Legendre polynomials transforms: from recurrence relations to Schoenberg’s theorem*, arXiv:1709.06082, September 17, 2017. - C. Asplund, R. Würtemberg, L. Höglund,
*Modeling tools for design of type-II superlattice photodetectors*, Infrared Physics & Technology 84 (2017) 21–27. - N. Courtier, J. Foster, S. O’Kane, A. Walker,
*Systematic derivation of a surface polarization model for planar perovskite solar cells*, August 30, 2017. - E. Carson, N. Higham,
*Accelerating the Solution of Linear Systems by Iterative Refinement in Three Precisions*, July 25, 2017. - Y. Kobayashi, T. Ogita, K. Ozaki,
*Acceleration of a Preconditioning Method for Ill-Conditioned Dense Linear Systems by Use of a BLAS-based Method*, Reliable Computing Journal, Volume 25, May 31, 2017. - D. Kressner, D. Lu and B. Vandereycken,
*Subspace acceleration for the Crawford number and related eigenvalue optimization problems*, April 25, 2017. - X. Xu, L. Li,
*Numerical stability of the C method and a perturbative preconditioning technique to improve convergence*, Journal of the Optical Society of America, Vol. 34, Issue 6, pp. 881-891 (2017). - E. Carson and N. Higham,
*A New Analysis of Iterative Refinement and its Application to Accurate Solution of Ill-Conditioned Sparse Linear Systems*, March 2017.

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by Pavel Holoborodko on June 23, 2017

Computer algebra systems are invaluable tools for modern researchers. Although commonly used CAS (Maple and Mathematica) are quite slow at numerical computations with extended precision, still they are main workhorses for doing tedious symbolic simplifications and manipulations on expressions.

However, with all the respect to substantial progress in the area, we want to draw attention to one of the not-so-obvious issues with symbolic simplifications – **implicit assumptions**. In a course of working with expression, symbolic engine makes certain assumptions about variables involved. This process is automatic and very helpful, as it takes this burden from user’s shoulders.

However, as always with any automation, picture is not that idealistic. Implicit assumptions made by software define the result we get, but nevertheless such assumptions are hidden from the user (at least by default) and not easily accessible. In some situations this leads to completely unexpected and wrong results. In this post we show one of the examples.

Read More

by Pavel Holoborodko on February 14, 2017

Recent papers citing the toolbox:

- B. Jin, B. Li, Z. Zhou,
*Correction of high-order BDF convolution quadrature for fractional evolution equations*, March 28, 2017. - S. Sarra,
*The Matlab Radial Basis Function Toolbox*, Journal of Open Research Software, March 27, 2017. - A. Shirin, I. Klickstein, F. Sorrentino,
*Optimal control of complex networks: Balancing accuracy and energy of the control action*, Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 27, Issue 4, April 2017. - Á. Rózsás, Z. Mogyorósi,
*The effect of copulas on time-variant reliability involving time-continuous stochastic processes*, Structural Safety, Volume 66, May 2017, Pages 94–105. - C. Asplund, R.M. von Würtemberg, L. Höglund,
*Modeling Tools For Design Of Type-II Superlattice Photodetectors*, Infrared Physics and Technology, 9 March 2017. - E.J. Kansa, P. Holoborodko,
*On the ill-conditioned nature of C-inf RBF strong collocation*, Engineering Analysis with Boundary Elements, Volume 78, May 2017, Pages 26–30. - M. Capek, V. Losenicky, L. Jelinek, M. Gustafsson,
*Validating the Characteristic Modes Solvers*, arXiv:1702.07037, February 24, 2017. - D. Clamond, D. Dutykh,
*Accurate fast computation of steady two-dimensional surface gravity waves in arbitrary depth*, February 13, 2017. - G. Veneziano, S. Yankielovicz, E. Onofri,
*A model for pion-pion scattering in large-N QCD*, arXiv:1701.06315, January 30, 2017. - S. Sarra, S. Cogar,
*An examination of evaluation algorithms for the RBF method*, Engineering Analysis with Boundary Elements, Volume 75, February 2017, Pages 36–45. - M. Barel, F. Tisseur,
*Polynomial eigenvalue solver based on tropically scaled Lagrange linearization*, The University of Manchester, December 25, 2016. - C. Zanoci, B. Swingle,
*Entanglement and thermalization in open fermion systems*, arXiv:1612.04840v1, 14 December 2016. - W.T. de Carvalho, C.A. Aguilar, N.A. Dumont,
*Some issues in the generalized nonlinear eigenvalue analysis of time-dependent problems in the simplified boundary element*. CILAMCE 2016 Proceedings of the XXXVII Iberian Latin-American Congress on Computational Methods in Engineering Suzana Moreira Ávila (Editor), ABMEC,Brasília, DF, Brazil, November 6-9, 2016.

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