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65F10  Iterative methods for linear systems (108 articles)

• Li, Jun; Xiong, Xiangtuan: A new block triangular preconditioner for three-by-three block saddle-point problem. (English). Applications of Mathematics, vol. 69 (2024), issue 1, pp. 67-91
• Zou, Lu; Lei, Yuan: The descent algorithms for solving symmetric Pareto eigenvalue complementarity problem. (English). Applications of Mathematics, vol. 68 (2023), issue 4, pp. 441-465
• Ali, Rashid; Pan, Kejia: The new iteration methods for solving absolute value equations. (English). Applications of Mathematics, vol. 68 (2023), issue 1, pp. 109-122
• Mollahasani, Somayeh; Panjeh Ali Beik, Fatemeh: Absolute value equations with tensor product structure: Unique solvability and numerical solution. (English). Applications of Mathematics, vol. 67 (2022), issue 5, pp. 657-674
• Shokrpour, Raheleh; Ebadi, Ghodrat: Extrapolated positive definite and positive semi-definite splitting methods for solving non-Hermitian positive definite linear systems. (English). Applications of Mathematics, vol. 67 (2022), issue 3, pp. 319-340
• Oktay, Eda; Carson, Erin: Mixed precision GMRES-based iterative refinement with recycling. (English). In: Chleboun, J., Kůs, P., Papež, J., Rozložník, M., Segeth, K. and Šístek, J. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Jablonec nad Nisou, June 19-24, 2022. Institute of Mathematics CAS, Prague, 2023. pp. 149-162
• Fakharzadeh Jahromi, Alireza; Nasseri Shams, Nafiseh: A new optimized iterative method for solving $M$-matrix linear systems. (English). Applications of Mathematics, vol. 67 (2022), issue 3, pp. 251-272
• Shekhar, Vaibhav; Mishra, Nachiketa; Mishra, Debasisha: On the convergence theory of double $K$-weak splittings of type II. (English). Applications of Mathematics, vol. 67 (2022), issue 3, pp. 341-369
• Gbikpi-Benissan, Guillaume; Magoulès, Frédéric: Resilient asynchronous primal Schur method. (English). Applications of Mathematics, vol. 67 (2022), issue 6, pp. 679-704
• Ortaggio, Marcello; Pravda, Vojtěch: Abelovu cenu za rok 2019 získala Karen Uhlenbecková. (Czech) [The 2019 Abel Prize awarded to Karen Uhlenbeck]. Pokroky matematiky, fyziky a astronomie, vol. 66 (2021), issue 1, pp. 1-10
• Strakoš, Zdeněk: Metoda konjugovaných gradientů jako dobrodružství jdoucí přes staletí. (Czech) [The Conjugate Gradient Method as a Journey Through Centuries]. Pokroky matematiky, fyziky a astronomie, vol. 65 (2020), issue 4, pp. 197-222
• Carson, Erin Claire: An adaptive $s$-step conjugate gradient algorithm with dynamic basis updating. (English). Applications of Mathematics, vol. 65 (2020), issue 2, pp. 123-151
• Giscard, Pierre-Louis; Pozza, Stefano: Lanczos-like algorithm for the time-ordered exponential: The $\ast $-inverse problem. (English). Applications of Mathematics, vol. 65 (2020), issue 6, pp. 807-827
• Ataei Delshad, Parandoosh; Lotfi, Taher: On the local convergence of Kung-Traub's two-point method and its dynamics. (English). Applications of Mathematics, vol. 65 (2020), issue 4, pp. 379-406
• Sousedík, Bedřich: On adaptive BDDC for the flow in heterogeneous porous media. (English). Applications of Mathematics, vol. 64 (2019), issue 3, pp. 309-334
• Tezaur, Radek; Vaněk, Petr: Improved convergence estimate for a multiply polynomially smoothed two-level method with an aggressive coarsening. (English). Applications of Mathematics, vol. 63 (2018), issue 6, pp. 629-641
• Futamura, Yasunori; Yano, Takahiro; Imakura, Akira; Sakurai, Tetsuya: A real-valued block conjugate gradient type method for solving complex symmetric linear systems with multiple right-hand sides. (English). Applications of Mathematics, vol. 62 (2017), issue 4, pp. 333-355
• Brousek, Jan; Fraňková, Pavla; Vaněk, Petr: Improved convergence bounds for smoothed aggregation method: linear dependence of the convergence rate on the number of levels. (English). Czechoslovak Mathematical Journal, vol. 66 (2016), issue 3, pp. 829-845
• Fraňková, Pavla; Mandel, Jan; Vaněk, Petr: Model analysis of BPX preconditioner based on smoothed aggregation. (English). Applications of Mathematics, vol. 60 (2015), issue 3, pp. 219-250
• Brandts, Jan H.; Reis da Silva, Ricardo: On the subspace projected approximate matrix method. (English). Applications of Mathematics, vol. 60 (2015), issue 4, pp. 421-452
• Vaněk, Petr; Brezina, Marian: Nearly optimal convergence result for multigrid with aggressive coarsening and polynomial smoothing. (English). Applications of Mathematics, vol. 58 (2013), issue 4, pp. 369-388
• Fraňková, Pavla; Hanuš, Milan; Kopincová, Hana; Kužel, Roman; Vaněk, Petr; Vastl, Zbyněk: A short philosophical note on the origin of smoothed aggregations. (English). In: Brandts, J., Korotov, S., Křížek, M., Šístek, J. and Vejchodský, T. (eds.): Applications of Mathematics 2013, In honor of the 70th birthday of Karel Segeth. Proceedings. Prague, May 15-17, 2013. Institute of Mathematics AS CR, Prague, 2013. pp. 67-76
• Čertíková, Marta; Burda, Pavel; Šístek, Jakub: Numerical comparison of different choices of interface weights in the BDDC method. (English). In: Brandts, J., Chleboun, J., Korotov, S., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Applications of Mathematics 2012, In honor of the 60th birthday of Michal Křížek. Proceedings. Prague, May 2-5, 2012. Institute of Mathematics AS CR, Prague, 2012. pp. 55-61
• Čertíková, Marta; Šístek, Jakub; Burda, Pavel: On selection of interface weights in domain decomposition methods. (English). In: Chleboun, J., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Dolní Maxov, June 3-8, 2012. Institute of Mathematics AS CR, Prague, 2013. pp. 35-44
• Rees, Tyrone; Stoll, Martin; Wathen, Andy: All-at-once preconditioning in PDE-constrained optimization. (English). Kybernetika, vol. 46 (2010), issue 2, pp. 341-360
• Hu, Guang-Da; Zhu, Qiao: Bounds of modulus of eigenvalues based on Stein equation. (English). Kybernetika, vol. 46 (2010), issue 4, pp. 655-664
• Gavalec, Martin; Zimmermann, Karel: Solving systems of two–sided (max, min)–linear equations. (English). Kybernetika, vol. 46 (2010), issue 3, pp. 405-414
• Franz, Sebastian; Liu, Fang; Roos, Hans-Görg; Stynes, Martin; Zhou, Aihui: The combination technique for a two-dimensional convection-diffusion problem with exponential layers. (English). Applications of Mathematics, vol. 54 (2009), issue 3, pp. 203-223
• von Petersdorff, Tobias; Schwab, Christoph: Sparse finite element methods for operator equations with stochastic data. (English). Applications of Mathematics, vol. 51 (2006), issue 2, pp. 145-180
• Kučera, Radek: Complexity of an algorithm for solving saddle-point systems with singular blocks arising in wavelet-Galerkin discretizations. (English). Applications of Mathematics, vol. 50 (2005), issue 3, pp. 291-308
• Cai, Xiao-Chuan; Marcinkowski, Leszek; Vassilevski, Panayot S.: An element agglomeration nonlinear additive Schwarz preconditioned Newton method for unstructured finite element problems. (English). Applications of Mathematics, vol. 50 (2005), issue 3, pp. 247-275
• Karátson, János: Mesh independent superlinear convergence estimates of the conjugate gradient method for some equivalent self-adjoint operators. (English). Applications of Mathematics, vol. 50 (2005), issue 3, pp. 277-290
• Bängtsson, Erik; Neytcheva, Maya: Numerical simulations of glacial rebound using preconditioned iterative solution methods. (English). Applications of Mathematics, vol. 50 (2005), issue 3, pp. 183-201
• Marek, Ivo: Schwarz-like methods for approximate solving cooperative systems. (English). Kybernetika, vol. 40 (2004), issue 5, pp. [611]-624
• Axelsson, Owe; Blaheta, Radim: Two simple derivations of universal bounds for the C.B.S. inequality constant. (English). Applications of Mathematics, vol. 49 (2004), issue 1, pp. 57-72
• Brandts, Jan; Křížek, Michal: Padesát let metody sdružených gradientů aneb Zvládnou počítače soustavy milionů rovnic o milionech neznámých?. (Czech) [Fifty years of the method of conjugate gradients or Will computers cope with]. Pokroky matematiky, fyziky a astronomie, vol. 47 (2002), issue 2, pp. 103-113
• Marek, Ivo; Mayer, Petr: Aggregation/disaggregation iterative methods applied to Leontev systems and Markov chains. (English). Applications of Mathematics, vol. 47 (2002), issue 2, pp. 139-156
• Klapka, Štěpán; Mayer, Petr: Aggregation/disaggregation method for safety models. (English). Applications of Mathematics, vol. 47 (2002), issue 2, pp. 127-137
• Blaheta, R.; Byczanski, P.; Kohut, R.: Composite grid finite element method: Implementation and iterative solution with inexact subproblems. (English). Applications of Mathematics, vol. 47 (2002), issue 2, pp. 83-100
• Šotová, Jarmila; Horová, Ivana: Some remarks on iterative methods for systems of linear equations. (English). Acta Mathematica et Informatica Universitatis Ostraviensis, vol. 9 (2001), issue 1, pp. 75-87
• Janka, Aleš: Algebraic domain decomposition solver for linear elasticity. (English). Applications of Mathematics, vol. 44 (1999), issue 6, pp. 435-458
• Tichý, Petr; Zítko, Jan: Derivation of BiCG from the conditions defining Lanczos' method for solving a system of linear equations. (English). Applications of Mathematics, vol. 43 (1998), issue 5, pp. 381-388
• Mayer, Günter: Epsilon-inflation with contractive interval functions. (English). Applications of Mathematics, vol. 43 (1998), issue 4, pp. 241-254
• Zítko, Jan: Using successive approximations for improving the convergence of GMRES method. (English). Applications of Mathematics, vol. 43 (1998), issue 5, pp. 321-350
• Křížek, Michal; Práger, Milan; Vitásek, Emil: Spolehlivost numerických výpočtů. (Czech) [Reliability of numerical calculations]. Pokroky matematiky, fyziky a astronomie, vol. 42 (1997), issue 1, pp. 8-23
• Lakić, Slobodan: A one parameter method for the matrix inverse square root. (English). Applications of Mathematics, vol. 42 (1997), issue 6, pp. 401-410
• Zítko, Jan: Combining the preconditioned conjugate gradient method and a matrix iterative method. (English). Applications of Mathematics, vol. 41 (1996), issue 1, pp. 19-39
• Hoppe, Ronald H.W.; Wohlmuth, Barbara: Efficient numerical solution of mixed finite element discretizations by adaptive multilevel methods. (English). Applications of Mathematics, vol. 40 (1995), issue 3, pp. 227-248
• Vaněk, Petr: Fast multigrid solver. (English). Applications of Mathematics, vol. 40 (1995), issue 1, pp. 1-20
• Křížková, Jitka; Vaněk, Petr: Explicit conjugate gradient method with preconditioning. (English). Applications of Mathematics, vol. 39 (1994), issue 4, pp. 309-316
• Vaněk, Petr: Multi-level method in eigenvalue problem. (English). Applications of Mathematics, vol. 39 (1994), issue 4, pp. 259-267
• Křížková, Jitka; Vaněk, Petr: Multigrid method with preconditioning on coarse level. (English). Applications of Mathematics, vol. 39 (1994), issue 5, pp. 365-373
• Šisler, Miroslav: On iterative methods of higher order for systems of linear algebraic equations. (English). Applications of Mathematics, vol. 39 (1994), issue 4, pp. 287-298
• Křížková, Jitka; Vaněk, Petr: Preconditioning of conjugate gradients by multigrid solver. (English). Applications of Mathematics, vol. 39 (1994), issue 5, pp. 357-364
• Heinrichs, Wilhelm: Spectral methods for singular perturbation problems. (English). Applications of Mathematics, vol. 39 (1994), issue 3, pp. 161-188
• Douglas, Jim; Hensley, Jeffrey L.; Roberts, Jean E.: An alternating-direction iteration method for Helmholtz problems. (English). Applications of Mathematics, vol. 38 (1993), issue 4, pp. 289-300
• Hanke, Martin; Hochbruck, Marlis; Niethammer, Wilhelm: Experiments with Krylov subspace methods on a massively parallel computer. (English). Applications of Mathematics, vol. 38 (1993), issue 6, pp. 440-451
• Mayer, Günter; Pieper, Lars: A necessary and sufficient criterion to guarantee feasibility of the interval Gaussian algorithm for a class of matrices. (English). Applications of Mathematics, vol. 38 (1993), issue 3, pp. 205-220
• Práger, Milan: A two parameter iterative method for solving algebraic systems of domain decomposition type. (English). Applications of Mathematics, vol. 38 (1993), issue 6, pp. 470-478
• Spedicato, Emilio; Vespucci, Maria Teresa: Variations on the Gram-Schmidt and the Huang algorithms for linear systems: A numerical study. (English). Applications of Mathematics, vol. 38 (1993), issue 2, pp. 81-100
• Míka, Stanislav; Vaněk, Petr: Acceleration of convergence of a two-level algebraic algorithm by aggregation in smoothing process. (English). Applications of Mathematics, vol. 37 (1992), issue 5, pp. 343-356
• Vaněk, Petr: Acceleration of convergence of a two-level algorithm by smoothing transfer operators. (English). Applications of Mathematics, vol. 37 (1992), issue 4, pp. 265-274
• Míka, Stanislav; Vaněk, Petr: A modification of the two-level algorithm with overcorrection. (English). Applications of Mathematics, vol. 37 (1992), issue 1, pp. 13-28
• Moszyński, Krzysztof: Remarks on polynomial methods for solving systems of linear algebraic equations. (English). Applications of Mathematics, vol. 37 (1992), issue 6, pp. 419-436
• Práger, Milan: An iterative method of alternating type for systems with special block matrices. (English). Applications of Mathematics, vol. 36 (1991), issue 1, pp. 72-78
• Šisler, Miroslav: Über die Konvergenzoptimierung eines symmetrischen Iterationsverfahrens. (German) [On the convergence optimization for a symmetric iteration method]. Applications of Mathematics, vol. 36 (1991), issue 1, pp. 21-31
• Šisler, Miroslav: Über die Konvergenz eines symmetrischen Iterationsverfahren für lineare Gleichungssysteme. (German) [On the convergence of a symmetric iterative method for systems of linear equations]. Aplikace matematiky, vol. 35 (1990), issue 6, pp. 471-480
• Šisler, Miroslav: Über ein mehrparametriges Iterationsverfahren für lineare algebraische Gleichungssysteme. (German) [On a multi-parameter iteration method for systems of linear algebraic equations]. Aplikace matematiky, vol. 35 (1990), issue 5, pp. 337-349
• Šisler, Miroslav: Beitrag zu mehrparametrigen Iterationsverfahren für spezielle lineare Gleichungssysteme. (German) [Contribution to multiparameter iterative methods for special systems of linear equations]. Aplikace matematiky, vol. 34 (1989), issue 4, pp. 265-273
• Axelsson, O.: Condition number estimates for elliptic difference problems with anisotropy. (English). In: Kurzweil, Jaroslav (ed.): Equadiff 7. Proceedings of the 7th Czechoslovak Conference on Differential Equations and Their Applications held in Prague, 1989. BSB B.G. Teubner Verlagsgesellschaft, Leipzig, 1990. pp. 218-224
• Herceg, Dragoslav; Cvetković, Ljiljana: Convergence of the accelerated overrelaxation method. (English). Aplikace matematiky, vol. 34 (1989), issue 6, pp. 475-479
• Šisler, Miroslav: Über die Verallgemeinerung eines gewissen Iterationsverfahrens für die Lösung spezieller linearer algebraischer Gleichungssysteme. (German) [On a generalization of a certain iterative method for the solution of special systems of linear algebraic equations]. Aplikace matematiky, vol. 34 (1989), issue 5, pp. 345-350
• Zítko, Jan: Two step extrapolation and optimum choice of relaxation factor of the extrapolated S.O.R. method. (English). Aplikace matematiky, vol. 33 (1988), issue 3, pp. 177-196
• Herzberger, Jürgen: Ein effizienter Algorithmus zur iterativen Einschliessung der inversen Matrix. (German) [An efficient algorithm for the iterative inclusion of the inverse matrix]. Aplikace matematiky, vol. 32 (1987), issue 4, pp. 271-275
• Blaheta, Radim: A multilevel method with correction by aggregation for solving discrete elliptic problems. (English). Aplikace matematiky, vol. 31 (1986), issue 5, pp. 365-378
• Šisler, Miroslav: Über ein mehrparametriges Iterationsverfahren für lineare Gleichungssysteme mit einer dünnen Matrix. (German) [A multi-parameter iterative method for systems of linear algebraic equations with sparse matrix]. Aplikace matematiky, vol. 31 (1986), issue 6, pp. 420-426
• Vajteršic, Marián: Some iterative Poisson solvers applied to numerical solution of the model fourth-order elliptic problem. (English). Aplikace matematiky, vol. 30 (1985), issue 3, pp. 176-186
• Práger, Milan: The method of fictitious right-hand sides. (English). Aplikace matematiky, vol. 29 (1984), issue 5, pp. 384-389
• Iusem, A.; de Pierro, A.: On the set of weighted least squares solutions of systems of convex inequalities. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 25 (1984), issue 4, pp. 667-678
• Segeth, Karel: On the choice of iteration parameters in the Stone incomplete factorization. (English). Aplikace matematiky, vol. 28 (1983), issue 4, pp. 295-306
• Šisler, Miroslav: Über ein mehrparametriges Iterationsverfahren für $p$-zyklische lineare Gleichungssysteme. (German) [On a multiparameter iteration method for $p$-cyclic systems of linear equations]. Aplikace matematiky, vol. 28 (1983), issue 1, pp. 44-54
• Šisler, Miroslav: Über ein Überrelaxationsverfahren für $p$-zyklische lineare Gleichungssysteme. (German) [On an overrelaxation method for $p$-cyclic systems of linear equations]. Aplikace matematiky, vol. 28 (1983), issue 4, pp. 249-261
• Šisler, Miroslav: Beitrag zu mehrparametrigen Iterationsverfahren. (German) [A contribution to multiparametric iterative methods]. Aplikace matematiky, vol. 27 (1982), issue 4, pp. 277-284
• Červ, Václav; Segeth, Karel: A comparison of the accuracy of the finite-difference solution to boundary value problems for the Helmholtz equation obtained by direct and iterative methods. (English). Aplikace matematiky, vol. 27 (1982), issue 5, pp. 375-390
• Sloboda, Fridrich: An imperfect conjugate gradient algorithm. (English). Aplikace matematiky, vol. 27 (1982), issue 6, pp. 426-432
• Šisler, Miroslav: Über die Konvergenzbeschleunigung des verallgemeinerten Oberrelaxationsverfahrens. (German) [On the convergence acceleration of the generalized overrelaxation method]. Aplikace matematiky, vol. 27 (1982), issue 1, pp. 17-26
• Axelsson, O.: On the iterative solution of finite element systems of equations. (English). In: Greguš, Michal (ed.): Equadiff 5. Proceedings of the Fifth Czechoslovak Conference on Differential Equations and Their Applications held in Bratislava, August 24-28, 1981. BSB B.G. Teubner Verlagsgesellschaft, Leipzig, 1982. pp. 25-29
• Šisler, Miroslav: Über eine Modifikation eines verallgemeinerten Überrelaxationsverfahrens. (German) [On a modification of a generalized overrelaxation method]. Aplikace matematiky, vol. 24 (1979), issue 5, pp. 348-354
• Sloboda, Fridrich: A parallel projection method for linear algebraic systems. (English). Aplikace matematiky, vol. 23 (1978), issue 3, pp. 185-198
• Šisler, Miroslav: Über ein Iterationsverfahren für die Lösung spezieller linearer Gleichungssysteme mit einer zyklischen Matrix. (German) [On an iteration method for the solution of a special linear system of equations with a cyclic matrix]. Aplikace matematiky, vol. 23 (1978), issue 4, pp. 295-299
• Il'in, V.: Gradient alternating-direction methods. (English). In: Fábera, Jiří (ed.): Equadiff IV. Czechoslovak Conference on Differential Equations and Their Applications. Proceedings, Prague, August 22-26, 1977. Springer-Verlag, Berlin, 1979. pp. [160]-169
• Marek, Ivo; Zítko, Jan: Ljusternik acceleration and the extrapolated S.O.R. method. (English). Aplikace matematiky, vol. 22 (1977), issue 2, pp. 116-133
• Šisler, Miroslav: Bemerkungen zur Optimierung eines zweiparametrigen Iterationsverfahrens. (German) [Remarks on optimization of a two-parametric iteration method]. Aplikace matematiky, vol. 21 (1976), issue 3, pp. 213-220
• Šisler, Miroslav: Über die Optimierung eines zweiparametrigen Iterationsverfahrens. (German) [On the optimization of a two-parametric iteration method]. Aplikace matematiky, vol. 20 (1975), issue 2, pp. 126-142
• Zítko, Jan: Extrapolation of S. O. R. iterations. (English). Aplikace matematiky, vol. 19 (1974), issue 2, pp. 72-89
• Young, D. M.: Iterative methods for solving large systems of linear equations. (English). Acta Universitatis Carolinae. Mathematica et Physica, vol. 15 (1974), issue 1, pp. 179-188
• Sloboda, F.: Note about the parallel projection method for solution of system of linear algebraic equations. (English). Acta Universitatis Carolinae. Mathematica et Physica, vol. 15 (1974), issue 1, pp. 157-158
• Marek, I.: A reduction method for approximate solving large elliptic systems. (English). Acta Universitatis Carolinae. Mathematica et Physica, vol. 15 (1974), issue 1, pp. 97-102
• Ostrowski, A. M.: Über Fehlerabschaetzungen a priori und a posteriori. (German). Acta Universitatis Carolinae. Mathematica et Physica, vol. 15 (1974), issue 1, pp. 111-115
• Šisler, Miroslav: Bemerkungen zur Optimierung eines gewissen Iterationsverfahrens. (German) [Remarks on optimization of certain iteration method]. Aplikace matematiky, vol. 18 (1973), issue 5, pp. 315-324
• Šisler, Miroslav: Über die Konvergenz eines gewissen Iterationsverfahrens für zyklische Matrizen. (German) [On the convergence of certain iteration method for cyclic matrices]. Aplikace matematiky, vol. 18 (1973), issue 2, pp. 89-98
• Šisler, Miroslav: Über die Konvergenz eines zweiparametrigen Iterationsverfahrens. (German) [On the convergence of a two-parametric iteration method]. Aplikace matematiky, vol. 18 (1973), issue 6, pp. 452-461
• Šisler, Miroslav: Über ein zweiparametriges Iterationsverfahren. (German) [On a two-parametric iteration method]. Aplikace matematiky, vol. 18 (1973), issue 5, pp. 325-332
• Šisler, Miroslav: Über ein Iterationsverfahren für zyklische Matrizen. (German) [On one iteration method for cyclic matrices]. Aplikace matematiky, vol. 17 (1972), issue 3, pp. 225-233
• Šisler, Miroslav: Über die Konvergenz von Iterationsverfahren. (German) [On the convergence of iteration methods]. Aplikace matematiky, vol. 16 (1971), issue 1, pp. 10-23
• Marek, Ivo: On a method of D. Marsal for equations with positive operators. (English). Aplikace matematiky, vol. 15 (1970), issue 6, pp. 413-417
• Liebl, Petr: Einige Bemerkungen zur numerischen Stabilität von Matrizeniterationen. (German) [Some remarks on numerical stability of matrix iteration]. Aplikace matematiky, vol. 10 (1965), issue 3, pp. 249-254
• Bílý, Josef: Solution of system of linear equations with large coefficients in the diagonal. (English). Aktuárské vědy, vol. 8 (1948), issue 3, pp. 114-127