LINEAR ALGEBRA

Author: DAZA FERNANDEZ VANESSA.
Year: 2003.
University: POLITÉCNICA DE CATALUÑA [www.upc.edu].
Place of defense: SALA D'ACTES DE LA FME.
Place of preparation: FACULTAT DE MATEMATIQUES I ESTADISTICA SUD.

Author: Díez Machío Héctor.
Year: 2005.
University: LEÓN [www.unileon.es].
Place of defense: Escuela de Ingeniería Industrial e Informática.
Place of preparation: Escuela de Ingeniería INdustrial e Informática.

Summary: SCOPE OF THE STUDY OF THE MACHINES ARE THE THESIS. ARE STUDYING THREE TYPES OF MACHINES. DYNAMIC LINEAR SYSTEMS ON HIGHER ORDER OF RINGS, THE DYNAMIC CUÁNTICOS AND SYSTEMS FOR MACHINERY SECUENCIALES FINITAS (AUTÓMATAS FINITOS). FOR THE FIRST KIND OF MACHINERY IS STUDYING THE PROBLEMS OF CARACTERIZAR THE ACCESSIBILITY AND THE SEARCH FOR INVARIANTES THROUGH EQUIVALENCE FEEDBACK. THE RESULTS OBTAINED GENERALIZAN RESULTS KNOWN FOR DYNAMIC OF ORDER ONE SYSTEMS. FOR THE SECOND TYPE OF MACHINES, MUCH LESS ESTUDIADAS, SE TRATAN THE PROBLEM THE SEARCH FOR FORM CANÓNICAS. PROPOSED SOLUTIONS FOR SYSTEMS IMPERTURBADOS AND SYSTEMS WITH UNIQUE CAMP EXTERNAL CONTROL. FORMS CANÓNICAS LEARNED ARE USED TO RESOLVE THE EQUATION DYNAMICS OF SUCH SYSTEMS. FOR THE THIRD KIND OF MACHINERY IS STUDYING SIMULTÁNEAMENTE MACHINES WITH CLASSICAL PERFORMANCE AND CUÁNTICO. PROPOSED TO BE A MODEL FOR MACHINE SECUENCIAL FINITA AND DEMUESTRA THAT MODEL GENERALIZA MODELS OF AUTÓMATAS FINITOS DETERMINISTAS, AUTÓMATAS PROBABILÍSTICAS AND MODELS OF KEY AUTÓMATAS CUÁNTICOS. HE DESCRIBES THE MEMBERSHIP IN CASCADA AND DEMUESTRA THAT THE MODEL IS Consistency WITH THIS OPERATION. ALSO THIS PRESENTS THE NEW MODEL OF POWER COMPOSICIONES WORKING WITH MACHINERY CLÁSICAS And CUÁNTICAS SIMULTÁNEAMENTE. FINALLY BE TREATED THE PROBLEM OF EQUIVALENCE FOR STATES AND LEAVES OPEN THE PROBLEM OF CALCULATE THE FORM FINITA WHEN TWO STATES OF THESE MACHINES ARE EQUIVALENT. HE OFFERS A CONJETURA FOR SUCH PROBLEM. SCOPE OF THE STUDY OF THE MACHINES ARE THE THESIS. ARE STUDYING THREE TYPES OF MACHINES. DYNAMIC LINEAR SYSTEMS ON HIGHER ORDER OF RINGS, THE DYNAMIC CUÁNTICOS AND SYSTEMS FOR MACHINERY SECUENCIALES FINITAS (AUTÓMATAS FINITOS). FOR THE FIRST KIND OF MACHINERY IS STUDYING THE PROBLEMS OF CARACTERIZAR THE ACCESSIBILITY AND THE SEARCH FOR INVARIANTES THROUGH EQUIVALENCE FEEDBACK. THE RESULTS OBTAINED GENERALIZAN RESULTS KNOWN FOR DYNAMIC OF ORDER ONE SYSTEMS. FOR THE SECOND TYPE OF MACHINES, MUCH LESS ESTUDIADAS, SE TRATAN THE PROBLEM THE SEARCH FOR FORM CANÓNICAS. PROPOSED SOLUTIONS FOR SYSTEMS IMPERTURBADOS AND SYSTEMS WITH UNIQUE CAMP EXTERNAL CONTROL. FORMS CANÓNICAS LEARNED ARE USED TO RESOLVE THE EQUATION DYNAMICS OF SUCH SYSTEMS. FOR THE THIRD KIND OF MACHINERY IS STUDYING SIMULTÁNEAMENTE MACHINES WITH CLASSICAL PERFORMANCE AND CUÁNTICO. PROPOSED TO BE A MODEL FOR MACHINE SECUENCIAL FINITA AND DEMUESTRA THAT MODEL GENERALIZA MODELS OF AUTÓMATAS FINITOS DETERMINISTAS, AUTÓMATAS PROBABILÍSTICAS AND MODELS OF KEY AUTÓMATAS CUÁNTICOS. HE DESCRIBES THE MEMBERSHIP IN CASCADA AND DEMUESTRA THAT THE MODEL IS Consistency WITH THIS OPERATION. ALSO THIS PRESENTS THE NEW MODEL OF POWER COMPOSICIONES WORKING WITH MACHINERY CLÁSICAS And CUÁNTICAS SIMULTÁNEAMENTE. FINALLY BE TREATED THE PROBLEM OF EQUIVALENCE FOR STATES AND LEAVES OPEN THE PROBLEM OF CALCULATE THE FORM FINITA WHEN TWO STATES OF THESE MACHINES ARE EQUIVALENT. HE OFFERS A CONJETURA FOR SUCH PROBLEM.

Author: CORTÉS UTRILLAS VANESA.
Year: 2006.
University: ZARAGOZA [www.unizar.es].
Place of defense: FACULTAD DE CIENCIAS.
Place of preparation: FACULTAD DE CIENCIAS.

Summary: This memory is part of the field of study of numerical methods suited to structured arrays, which shows a strong and growing research activity. Classes structured arrays considered relate to properties sign. Some of the classes of matrices that will be explored more in the memory are those of the parent signo-regulares and strictly signo-regulares containing latter both matrices totally positive as entirely negative. Recall that an array mxn is called (strictly) signo-regular if, for each k = 1 ,..., min (m, n), all under Order k have the same sign (strict). It examines the growth factor in the elimination of Gauss with different strategies pivoting. Some of the strategies pivoting considered are new and intermediate between pivoting partial pivoting and strategy recently introduced, the so-called pivot "rook." In contrast to the partial pivoting, which is not "backward" stable for the elimination of Gauss-Jordan, we see that these strategies intermediate yes they are. Besides showing a good performance for the elimination of Gauss.Usando called average growth factor we see that these strategies are already very competitive intermediate compared with more expensive pivoting "rook." We also analyzed the growth factor and other aspects of the strategies pivoting partial scaling, as well as its economic implementation in the case of applying them to special classes of matrices, such as the important class of M-matrices. In addition, we propose a strategy for pivoting rows (called dos-determinantal) associated with the elimination of Neville for arrays signo-regulares. We see that this strategy is optimal growth factor and can be applied with a reduced computational cost (less than the pivot partial); addition, this strategy produces the same exchanges rows strategies pivoting partial climbed for the elimination of Neville. Special mention that this strategy preserves signo-regularidad along the process of elimination. The characterization that we presented to the parent strictly signo-regulares by eliminating Neville with this new strategy allows us to provide a robust test that checks for the strict signo-regularidad an array anyone. Finally, we believe the parent descomposiciones strictly signo-regulares. Between descomposiciones analyzed, we might mention the LDU, QR, the DPS, and the polar call simétrica-triangular. We also characterizations of this class of matrices through some of its factoring. In particular, we see that in many situations, these characterizations are simplified considerably, as for example in the case of arrays totally negative.