Prezentare MECIPT, Cluj. maruster

1. Mathematics of Computation: -numerical methods for nonlinear equations (clasification ACM: G.1.5); -convergence and stability (clasification ACM: G.1.7) 2. Software, programing languages, compilers (clasification ACM: D.3.4); 3. Theory of computing, formal languages, (clasification ACM: F.4.3); 4. Mathematical software (clasification ACM: G.4).

   Results

2. The study of some iterative methods of convex combination type (between the current iteration and the mapping value in the current iteration), for solving nonlinear equations in Hilbert spaces ([1],[2],[3],[4],[5],[6]. These results generalize certain known results obtained by Petryshyn, Senter, Dotson, etc. The main convergence conditions are the quasi-nonexpasivity and the closeness in the origin of the space (without continuity). The method is applied to the computation of the best approximation polynomial in the sense of Thebychev. Most of these results are contained in the PhD thesis [7].
3. The investigation of projection algorithms for solving convex feasibility problems [6]; conditions in which the projection algorithm considered by Bergman, Agmon, Motzkin, Schoenberg, and recently by Bauschke, Combettes, Borwein (between 2001-2003), etc., that are known to converge only weakly (in Hilbert spaces), becomes strongly convergent. Application to mathematical programming, image processing, computer tomograpfy, etc.
4. The study of some methods of gradient and conjugate gradient type for sparse nonlinear equations in finite dimensional spaces [8],[9],[10],[11]. Significant results: necessary conditions that gradient method (Fridman variant ) have superlinear convergence; the estimation of optimal weight factor in conjugate gradient methods (the asymptotic behavior of this factor is like the Fletcher-Reeves factor in unconstrained optimization problem); a new method of conjugate gradient type, called the NFCG method (Nonlinear Fridman Conjugate Gradient), with improved performances (number of iterations, computing effort, the possibility of exploiting the sparseness of the system).
   1. The analysis of the total stability of gradient like methods for nonlinear equations with respect to strongly consistent disturbances of the Jacobian.[12]. The main results: these disturbances does not have a dramatic influence about the convergence of the computed sequence, but the super-linear convergence can be lost.
5. The estimation of stability region for autonomous nonlinear differential systems [13]. The asymptotic behavior of the successive approximations obtained via some expansion scheme of trajectory reversing type is investigated and some numerical algorithms for the computing the boundary of stability region are given.
6. Măruşter, Şt., Algoritm pentru determinarea celei mai bune soluţi aproximative a unui sistem liniar, Anal. Univ. Timişoara, seria Şt. Mat. Vol. IX, f. 1 (1971), 84-89.
7. Măruşter, Şt., Sur le calcul des zeros d”un operateur discontinu par iteration, Canad. Math. Bull., Vol. 16, no. 4 (1973), 541-544.
8. Măruşter, Şt., Relaxation algorithm for nonlinear inequalities, Proceedings of convexity and approximation, Cluj-Napoca (1975), 45-53.
9. Măruster, Şt., An iterative method for nonlinear difference equations, Anal. Univ. Timişoara, seria Şt. Mat. Vol. XIV, f. 2 (1979), 117-124.
10. Măruşter, Şt., Quasi-nonexpansivity and two classical methods for solving nonlinear equations, Proc. Amer. Math. Soc., Vol. 62, no. 1 (1977), 119-123.
11. Măruşter, Şt., The solution by iteration of nonlinear equations in Hilbert space, Proc. Amer. Math. Soc., Vol. 63, no. 1 (1977), 69-73.
12. Măruşter,Şt., Numerical computation of the zeros of monotone nonlinear operators, PhD thesis, Cluj, 1964.
13. Măruşter, Şt., Popovici, P., Generalized gradient method, Anal. Univ. Timişoara, seria Şt. Mat. Vol. XXI, f. 1-2 (1983), 85-94
14. Măruşter, Şt., On the two step gradient method for nonlinear equations, part I, Proceedings of the colloquium on approximation and optimization, Cluj- Napoca, 1984, 88-104.
15. Măruşter, Şt., On the solution of nonlinear equations; methods and programs, Proceedings of the IV Conference of Operator Theory, Timişoara, 1984, 207-221.
16. Măruşter, Şt., On the two step gradient method for nonlinear equations, part II, Anal. Univ. Timişoara, seria Şt. Mat. Vol. XXV, f. 3 (1987), 69-84.
17. Măruşter, Şt., The stability of gradient-like methods, Aplied Mathematics and Computation
    1. St. Maruster, Asimptotic behavior of successive approximation given by expansinon schemes, Rev. d'Anal. Num. Theor. Approx, Vol. 30, Nr. 1, (2002), pp. 89-101.

Publications

Articles in journals with inpact factor

Maruster, St., Popirlan, C., On the regularity condition in convex feasibility Problem, Nonlinear Analysis, TMA, article in press.

Maruster, St., Popirlan, C., On the Mann-type iteration and convex feasibility problem, J. Comput. Appl. Math., Vol. 212, no. 2 (2008), pp. 390-396.

Maruster, St., Popirlan, C., Strong convergence of the projection method in convex feasibility problem, Proceedings of 9th SYNASC (20070, 376-380

Măruşter, Şt., The stability of gradient-like methods, Aplied Mathematics and Computation, Vol 117 (2001), 103-115.

Măruşter, Şt., Quasi-nonexpansivity and two classical methods for solving nonlinear equations, Proc. Amer. Math. Soc., Vol. 62, no. 1 (1977), 119-123.

Măruşter, Şt., The solution by iteration of nonlinear equations in Hilbert space, Proc. Amer. Math. Soc., Vol. 63, no. 1 (1977), 69-73.

Măruşter, Şt., Sur le calcul des zeros d”un operateur discontinu par iteration, Canad. Math. Bull., Vol. 16, no. 4 (1973), 541-544.

Grun, U., Măruşter, Şt., Die Messung Localer Seitunverranderlicher Inductionen mit Siforming Gedrehten Feldplatten, Archiv fur Technisches Messen, Blat Vol. 392, nr. 5 (1972), 27-30.

Articles in other journals

Maruster, L., Maruster, St., On convex feasibility problem, Carpathian J. Math., Vol. 21 (2005), 83-87.

Măruşter, St., Asimptotic behavior of successive approximation given by expansinon schemes, Rev. d’Anal. Num. Theor. Approx, Vol. 30, N0.1 (2002), pp. 89-101.

Maruster, St., Quasi-nonexpansivity and the convex feasibility problem, Ann. Univ. “A.I.Cuza”, Iasi (to appear)

Măruşter, Şt., On the conjugate gradient method for nonlinear equations, Ann Univ. Timisoara, Ser. Math-Info, Vol. XXXVII (1999), 37-43.

Maruster, St.; On the expansion schemes in trajectory reversing method, Revue d,Analyse Numerique et de la Theorie de l,Approximation (to apear)

Măruşter, Şt., On the conjugate gradient method for nonlinear equations, Ann Univ. Timisoara, Ser. Math-Info, Vol. XXXVII (1999), 37-43.

Balint, Şt., Schlett, Z., Măruşter, Şt., Balint, A., Jădăneanţu, I., Size stability in groing single cristaline shests, part II, Anal. Univ. Timişoara, seria Şt. Mat. Vol. XXVI, f. 3 (1988), 3-15.

Măruşter, Şt., Experiments on the regions of asymptotic stability, Anal. Univ. Timişoara, seria Şt. Mat. Vol. XXVI, f. 3 (1988), 16-33.

Măruşter, Şt., On the two step gradient method for nonlinear equations, part II, Anal. Univ. Timişoara, seria Şt. Mat. Vol. XXV, f. 3 (1987), 69-84.

Măruşter, Şt., Popovici, P., Generalized gradient method, Anal. Univ. Timişoara, seria Şt. Mat. Vol. XXI, f. 1-2 (1983), 85-94

Măruster, Şt., An iterative method for nonlinear difference equations, Anal. Univ. Timişoara, seria Şt. Mat. Vol. XIV, f. 2 (1979), 117-124.

Perju, D., Kovacs, Fr., Măruşter, Şt., Unele aspecte ale utilizării calculatoruui MECIPT-1 la rezolvarea unor probleme din domeniul teoriei mecanismelor, Construcţia de maşini, Vol. 23, nr. 7 (1971), 415-420.

Măruşter, Şt., Algoritm pentru determinarea celei mai bune soluţi aproximative a unui sistem liniar, Anal. Univ. Timişoara, seria Şt. Mat. Vol. IX, f. 1 (1971), 84-89.

Kovacs, Fr., Perju, D., Măruşter, Şt., Miecovits, Şt., Sinteza unui mecanism pentru regulatorul motorului Diesel de 2500 CP fabricat la UCM Reşiţa, Bul. Şti. The. Inst. Pol. Timişoara, Vol. 15 (29), f. 1 (1970), 33-40

Farcaş, D., Gavrilescu, G., Măruşter, Şt., Autocod şi translator, Bul. Şti. The. Inst. Pol. Timişoara, Vol. 12 (26), f. 2 (1968), 347-358.

Kovacs, Fr., Măruşter, Şt., Perju, D., Uroş, D., Program pentru determinarea parametrilor cinematici ai mecanismelor patrulater articulat la calculatorul MECIPT-1, Bul. Şti. The. Inst. Pol. Timişoara, Vol. 12 (26), f. 1 (1967), 279- 289.

Papers at conferences

Maruster, St., Popirlan, C., On the projection method for convex feasibility problem, ICCAM (International Conference on Computational and Applied Mathematics), 10.07-15.06, 2006, Univ. Leuven, Belgium.

Maruster, St., Maruster, L., On the parallel implementation of the Block Gradient Algorithm for nonlinear equations, Proceeding of the 6th Symposium on Symbolic and Numeric Algorithms for Scientific Computing, 2004, pp. 242-249.

Maruster, St., Maruster, L., On the Mann iteration and applications, Proceedings of 26th Inter. Conference Information Technology and Interfaces, Dubrovnoc, Croatia, June, 2004.

Măruşter, Şt., Măruşter, L., The stability of steepest descent methods for systems of nonlinear equations, Proceedings of the International Conference on Information Technology Interfaces, Pola, Croatia, june 15-18, 1999, p. 359- 364.

St. Maruster, V. Negru, D. Petcu, C. Sandru, Intelligent front-end forsolving differential and non-linear equations, International Conference:Computer Algebra in Scientific Computing, St. Petersburg, April 20-24 1998,published in proceedings, pp. 91-95, to appear in Springer Verlag (extendedversion).

Măruşter, Şt., Negru, V., Şandru, C., CLIPS-Inteligent front-end for nonlinear equations solver, International Symposium ROSYCS”98, 11th Romanian Symposium on Computer Science, May 28-30, 1998, Iaşi, Romania.

St. Maruster, Numerical estimation of domain of asymptotical stability , International Conf. NMCM, Miscolk, Hungaria, june, 1998

Măruşter, Şt., Negru, V., Petcu., Şandru, C., INTENSE, Inteligent non-linear algebraic and differential equations solver, Internatoinal syimposium on system theory, robotics, computers and proces informatics – SINTES 9, June, 1998, Craiova, p. 38-45.

1. Negru, St. Maruster, S. Calin, M. Rotaru, Multiagent system forNESS, Research Report, Theoretical Computer Science Dept.,University of the West, September, 1998.
2. Negru, St. Maruster, C. Sandru, Intelligent system for non-linear simultaneous equations solving, RISC - Linz Report Series No. 98-19, December 1998

St. Maruster, Optimal weight factor in conjugate gradient methods, Workahop “Symbolic-Numeric Analysis of Differential Equations”, Prague, June 16- 18, 1997.

Măruşter, Şt., Negru, V., Şandru, C., Marin, M., Inteligent methods for solving non-linear systems of equations, Proceedings of ICAOR, International Conference in Numerical Analysis, Cluj, July, 1997.

St. Maruster, V. Negru, L. Maruster, C. Sandru, F. Berinde, M. Marin Intelligent methods selection for solving non-linear equations systems,International Conference in Numerical Analysis, Cluj, July 1997, publishedin proceedings.

St. Maruster, V. Negru, L. Maruster, Non-linear Equations SystemSolver, Research Report, Theoretical Computer Science Dept.,University of the West, September 1997.

1. Negru, St. Maruster, NESS - A decision trees implementation for nonlinear equations systems solver,Parallel Computing Seminar, RISC - Linz, Austria, November, 1994;

Măruşter, Şt., On the two step gradient method for nonlinear equations, part I, Proceedings of the colloquium on approximation and optimization, Cluj- Napoca, 1984, 88-104.

Măruşter, Şt., On the solution of nonlinear equations; methods and programs, Proceedings of the IV Conference of Operator Theory, Timişoara, 1984, 207- 221

Măruşter, Şt., Popovici, P., Asupra metodei direcţiilor alternate, Sesiunea comună de comunicşri ale cadrelor didactice şi studenţilor, Univ. Timişoara, martie, 1981

Jebelean, T., Măruşter, Şt., Negru, V., Compilator FORTRAN conversaţional, A III-a conferinţă a Centrelor de Calcul din reţeaua MEI, Cluj, august, 1980

Măruşter, Şt., Sur quelques methodes iteratives de type gradient, A IV-a conferinţă de teoria operatorilor, Timişoara, iunie, 1979.

Măruşter, Şt., Negru, V., Jebelean, T., Subsitem conversaţional pentru limbajele ASSIRIS; FORTRAN; COBOL, Sesiunea ştiinţifică anuală, Univ. Timişoara, oct. 1978.

Măruşter, Şt., Asupra metodei parabolelor interpolatoare pentru minimizarea funcţionalelor neliniare, Lucr. Sesiunii St. ale Centrului de Calcul Univ. Bucureşti, !978, 132-136

Măruşter, Şt., Asupra metodei direcţiilor alternate, Lucr. Sesiunii St. ale Centrului de Calcul Univ. Bucureşti, !978, 332-338.

Măruşter, Şt., Relaxation algorithm for nonlinear inequalities, Proceedings of convexity and approximation, Cluj-Napoca (1975), 45-53.

Măruşter, Şt., Rezolvarea numerică a unor ecuaţii neliniare în spaşii Hilbert reale, Simpozionul de teoria convexităţii şi aplicaţii la studiul problemelor de optimizare, Univ. “Babeş-Bolyai”, Cluj, iulie, 1975.

Măruşter, Şt., Utilizarea şirurilor poloneze în compilarea expresiilor aritmetice, Sesiunea Ştiinţifică IPT, mai, 1970.

Măruşter, Şt., Asupra trasării graficelor funcţiilor reprezentate parametric, Sesiunea Ştiinţifică IPT, mai, 1970.

Hoffman, I., Pop, V., Măruşter, Şt., Automat probabilistic ca regulator instruibil, Lcucrările Conferinţei II a Electricienior, secţia V Automatică, Bucureşti (1969), 521-531.

Gavrilescu, G., Mşruşter, Şt., Program de inversare a matricilor pentru calculatoare cu memorie mică, Sesiunea Ştiinţifică IPT, Martie, 1966, Timişoara.

Măruşter, Şt., Aplicarea metodei gradientului la calculul polinoamelor de cea mai bună aproximare, Colocviul “Utilizare calculatoarelor electronice în proiectare”, Februarie, !966, Timişoara

Scientific reports Institute e-Austria of Timisoara

Maruster, St., Popirlan, C., Quasi-nonexpansivity and convex feasibility problem, Tech. Reports, IeAT, no. 6, 2005

Maruster, St., Asynchronous iterative algorithms on computational grid, Tech. Reports, IeAT, nr.5, 2005.

Bonchis, C., Maruster, St., Reordering algorithm for preconditioning nonliner problems, Tech. Reports, IeAT, nr.2, 2005.

Maruster, St., Experiments on the local load balancing algorithms, Tech. Report, IeAT, Nr.5, 2004.

Scientific reports concerning the building of the romanian computer MECIPT-1 between 1965-1972

Kaufman, I., Farcaş, D., Gavrilescu, G., Măruşter, Şt., Micrositem de operare pentru clculatoarele MECIPT.

Gavrilescu, G., Măruşter, Şt., INEX- rutine de intrare/ieşire pentru calculatorul MECIPT-1.

Măruşter, Şt., Sistem de sincronizare/desincronizare a operaţiilor da intrre/ieşire pentru calculatorul MECIPT-1.

Măruşter, Şt., Sistem grafic 2D şi 3D pentru calculatoarele MECIPT.

Măruşter, Şt., Microsistem de operare cu gestionarea optimă a memoriei.

Măruşter, Şt., Rutine de calcul în virgulă mobilă.

Farcaş, D., Gavrilescu, G., Măruşter, Şt., Sistem de subprograme matematice: sisteme liniare, inversare de matrici, valori proprii, ecuaţii plinomiale, sisteme neliniare, Runge-Kuta, metode cu diferenţe pentru ecuaţii cu derivate parţiale, metoda celor mai mici petrate, calculul polinoamelor de cea mai bună aproximare în sensul lui Cebâşev. Obs. Calculul polinoamelor de cea mai bună aproximare a constituit punctul de plecare pentru teza de doctorat susţinută la Cluj în 1974.

Măruşter, Şt., Compilator FORTRAN cu optimizarea spaţiului de memerie.

Books (in romanian)

Cira, O., Maruster, St., Metode numerice pentru ecuatii neliniare, Ed. Matrix, Bucuresti, 2008.

Măruşter, Şt., Curs de proiectarea compilatoarelor, Ed. Univ. de Vest, Timişoara, 2000

Drăgan, M., Măruşter, Şt., Limbaje Formale, Ed. Eubeea, Timişoara, 1998.

Măruşter, Şt., Metode numerice în rezolvarea ecuaţiilor neliniare, Editura Tehnică, Bucureşti, 1981 (205 pagini).

Măruşter, Şt., Elemante ale sistemului de operare SIRIS-3, Editura Facla, Timişoara, 1980 (260 pagini).

Măruşter, Şt., Luca, L., Negru, V., Sisteme de operare, îndrumător de laborator, Tip. Univ. Timişoara, 1984 (124 pagini).

Măruşter, Şt., Curs de sisteme de operare şi teleprelucrare, Tip. Univ. Timişoara, 1979 (260 pagini).

CITARI

St. Maruster, The solution by iteration of nonlinear equation in Hilbert spaces, Proc. Amer. Math. Soc., Vol. 63, No. 1, (1977), pp 69-73

Chidume, C.E., Souza, G.De., Convergence of a Halpern-type iteration algorithm for a class of pseudo-contractive mappings, Nonlinear Analysis (to appear), 2008.

Mainge, P-E., Convex minimization over the fixed point set of demicontractive Mappings, Positivity (2008), DOI 10.1007/s11117-007-2066-x.

Ying Zhang, Yan Guo, Weak convergence theorems of three iterative methods for strictly pseudocontractive mappings of Browder- Petryshyn type, Hindawi Publishing Corporation, Fixed Point Theory and Applications, Vol. 2008, DOI: 10.1155/2008/672301.

Chidume, C.E., Abbas, M., Bashir, A., Convergence of the Mann iteration algorithm for a class of pseudo-contractive mappings, Appl. Math. Appl., Vol. 194, (2007), pp. 1-6.

Yongfu Su, Suhong Li, Composite implicit iteration process for common fixed Points of a finite family of strictly pseudocontractive maps, J. Math. Anal. Appl., Vol. 320, No. 2 (2006), pp. 882-891.

Su Yong-fu, Gu Guang-hui, Geometric results for implicit iteration process approximating common fixed points of strictly pseudocontractive mappings, Journal of Hebei University, Vol. 25, No. 5 (2005), pp. 458 – 460.

Su Yong-fu, Li Su-hong, System of implicit iteration for fixed points of a finite family of strictly pseudocontractive mappings, Journal of Tianjin Polytechnic University, Vol. 24, No. 6 (2005), pp. 47 – 49.

Osilike, M.O., Implicit iteration process for common fixed points of a finite family of strictly pseudocontractive mapps, J. Math. Anal. Appl., Vol. 294, no. 1 (2004), pp. 73-81;

Bradiev, I.B., Zadvornov, O.A., A decomposition method for variational inequalities of the second kind with strongly inverse monotone operators, Diff. Equations, Vol. 39, No. 7 (2003), pp. 936-944;

Bradiev, I.B., Zadvornov, O.A, Ismagilov L.A., On iterative regularizatin methods for variational inequalities of the second kind, Comput. Math. Appl. Math., Vol. 3, No. 2 (2003), pp. 223 – 232.

Combettes, P.L., Pannanen, T., Generalized Mann iterates for constructing fixed points in Hilbert spaces, J. Math. Annal. Appl., Vol. 275, No. 2 (2002), pp. 521-536;

Bauschke, H.H., Borwein, J.M., On the projection algorithms for solving convex feasibility problems, J. Math. Annal. Appl., Vol. 275, No. 2 (2002), pp. 521-536;

Bradiev, I.B., Zadvornov, O.A., Saddek, A.M., Convergence analysis of iterative methods for some variational inequalities with pseudomonotone operators, Diff. Equations, Vol. 37, No. 7 (2001), pp. 934-942;

Bauschke, H.H., Combettes, P.L., A weak-to-strong convergence principle for Fejer-monotone methods in Hilbert spaces, Math. Optimization Researche, Vol. 26, No. 2 (2001), pp. 248-264;

Osilike, M.O., Igbokwe, D.I., Weak and strong convergence theorems for fixed ponts of pseudocontractions and solutions of monotone type operator equations, Comp. Math. Appl., Vol. 40 (2000), pp. 559-567.

Osilike,M.O., Strong and weak convergence of the Ishikawa iteration method for a class of nonlinear equations, Bull. Korean Math. Soc., Vol. 37, No. 1 (2000), pp. 153-169.

Moore, C.S., Iterative approximation of fixed points of demicontractive maps, Technical Teport, Inter. Centre for Theoretical Physics, Trieste, Italy, November, 1998.

Bauschke H. H., The approximation of fixed points of compositions of nonexpansive mapings in Hilbert spaces, J. Math. Anal., Vol. 202 (No. 1): pp 150-159, 1996, 16R, VC684;

Chidume, C.E., An iterative method for nonlinear demiclosed monotone type operarors, Dynam. Systems Appl., Vol. 3, No. 3 (1994), pp. 349-355;

Vasin, V.V., Ill posed problems and iterative approximation of fixed points of pseudo-contractive mappings, Ill posed probems in natural science, 1992 VSP/TVP, pp. 214-223.

Chidume,C.E., An iterative method for nonlinear demiclosed monotone type operarors, Inter. Centre for Theoretical Phizics, Trieste, Italy, Researche report, No. 5, 1992.

Weng, Xinlong, The iterative solution of nonlinear equations in certain Banach spaces, J. Nigerian Math. Soc., Vol. 11, No. 1 (1992), pp. 1-7;

Chidume C. E., Fixed point iterations for nonlinear hammerstein equations involving nonexpansive and accretive mappings, I. J. PA. Math., Vol. 20 (no. 2): 129-135, 1989, 26R T6407;

Chidume, C.E., The solution by iteration of nonlinear equations in certain Banach spaces, J. Nigerian Math. Soc., Vol. 3, (1984), pp. 57-62;

Catinas,E.,