23
Algoritmos divide y vencerás para la resolución de sistemas lineales tridiagonales en un computador BSP Leandro Tortosa Grau 2000 Tesis de Doctorado Facultad: Escuela Politécnica Superior Director: Dr. Joan Josep Climent Coloma brought to you by CORE View metadata, citation and similar papers at core.ac.uk provided by Repositorio Institucional de la Universidad de Alicante

Algoritmos divide y vencerás para la resolución de sistemas lineales tridiagonales ... · 2016. 8. 20. · Algoritmos divide y vencerás para la resolución de sistemas lineales

  • Upload
    others

  • View
    0

  • Download
    0

Embed Size (px)

Citation preview

Page 1: Algoritmos divide y vencerás para la resolución de sistemas lineales tridiagonales ... · 2016. 8. 20. · Algoritmos divide y vencerás para la resolución de sistemas lineales

Algoritmos divide y vencerás para la

resolución de sistemas lineales tridiagonales en un computador BSP

Leandro Tortosa Grau

2000

Tesis de Doctorado Facultad: Escuela Politécnica Superior

Director: Dr. Joan Josep Climent Coloma

brought to you by COREView metadata, citation and similar papers at core.ac.uk

provided by Repositorio Institucional de la Universidad de Alicante

Page 2: Algoritmos divide y vencerás para la resolución de sistemas lineales tridiagonales ... · 2016. 8. 20. · Algoritmos divide y vencerás para la resolución de sistemas lineales

���������� �� ���� �

���� ��� � �� ������ �� �

����� ����� � �� �������� � �����

����� ��� ������ � �������� �� �

����������� �� ��� ��� ������� ����������

�� �� ����� ��� ���

����� ������

�� � ����� ���� ����� ������� ����

�������� ���� ���� ��� � ���� �� ������

Page 3: Algoritmos divide y vencerás para la resolución de sistemas lineales tridiagonales ... · 2016. 8. 20. · Algoritmos divide y vencerás para la resolución de sistemas lineales
Page 4: Algoritmos divide y vencerás para la resolución de sistemas lineales tridiagonales ... · 2016. 8. 20. · Algoritmos divide y vencerás para la resolución de sistemas lineales

���������� �� ���� �

���� ��� � �� ������ �� � ����� ����� � �� ��������

� �����

����� ��� ������ � �������� �� � ����������� �� ��� ��� ������� ����������

�� �� ����� ��� ���

� ����� �� � ����� ���� ����� �� ����� � ������ ��� �� �� � ���

���!����� ��� ������� ����� ����"

������ # $% � ���� �&� � $'''

Page 5: Algoritmos divide y vencerás para la resolución de sistemas lineales tridiagonales ... · 2016. 8. 20. · Algoritmos divide y vencerás para la resolución de sistemas lineales
Page 6: Algoritmos divide y vencerás para la resolución de sistemas lineales tridiagonales ... · 2016. 8. 20. · Algoritmos divide y vencerás para la resolución de sistemas lineales

��� ��� ��� ������ ������# ��� ��� ������� � (��) ������ � � � ������ ��� � �� ���� � �� ���������*�� ��� ��� ����

���+���� � �� (��) ������ � ������ #

�����,���

-� �� �� � �� � ����� ��������� ���� �������� ���� �� ���������� � ����� ������� ����������� �� �� ��������� ���# .�

���� � ���/��� &�0� �� ��� ���!��# � � � ������ ��� � �� ���� � �� ���������*�� ��� ��� ���� ���+���� � �� (��) ������ � ������ #

��� � ��� ������ ��� ������� ����� ����# 1 ��������1 �� � ��� ���� ����� �� ����� � ������ � ��� �� �� � �� ���!�����" ����

2� ����� # � �������� ��� � �� � �������!�� )�� �� # ������/� �� �� � �����!�� � �� � ���� � ��� �������� ��� �� ������!�� � ���������

� �� (��) ������ � ������ # +������ � �� � �� � ���+����"

������ # $% � ���� �&� � $'''"

,��"� ���� ��� � ���� �� ������

Page 7: Algoritmos divide y vencerás para la resolución de sistemas lineales tridiagonales ... · 2016. 8. 20. · Algoritmos divide y vencerás para la resolución de sistemas lineales
Page 8: Algoritmos divide y vencerás para la resolución de sistemas lineales tridiagonales ... · 2016. 8. 20. · Algoritmos divide y vencerás para la resolución de sistemas lineales

� ������� ��� � �������� �������� �� ���

�� ��� ������������� �� ����� ��������

���� ���� ����� ���������

Page 9: Algoritmos divide y vencerás para la resolución de sistemas lineales tridiagonales ... · 2016. 8. 20. · Algoritmos divide y vencerás para la resolución de sistemas lineales
Page 10: Algoritmos divide y vencerás para la resolución de sistemas lineales tridiagonales ... · 2016. 8. 20. · Algoritmos divide y vencerás para la resolución de sistemas lineales

�� ���� � �����# 2�� �� 3�� ��� �� ����� ���� ��� �� ��� ��� ���� ��� � ���� �� ��� ����� ��� �������� ����# ���� 0�� 1 �������

2� � .� ����������� � �� ����� � ����� ���� �4���" �� ���� ���� 1 .�&������ .�� ���� � � ������� � ���� 2� �� ���&�0� �� ���� �

&� � �� ���# ��!5 ���� �� ���� ��������� � ���&�0� 1 ����������"

�� � ����� �����# ����� � � � ������ 6����� �� ������� 1 ����� ���!�� ������" 7� ���� � �����4� �� � � ��� � ��� ����� ���) �!5�"

������ . ��� � � &���� ��� �� ��!5�� 1 . ��� �� ���� ��� � � ����� � ������� � � ���&�0� ������"

(�� � ����� � �� 2� ������ ���.� ���� ��� ������ 1 ���� � ����� � 8���)���� �����# � �� 2� �����!5 � 8�) ��� ������

��� �/�&� �� ���� �� ��� �� 1# ��� �����# �� 3� �� ���� �� ����" ���� � ���� � �������� ��� � ��� ��� ���� ��� � ���� ��"

-�� �� ���&�! � ����� � � � ������� � ������ �� ���+��/� 1 ���1� 2� � .�� �����������# �� 2� .� � ������� ����� ���� ����

�!5# �� � � .�� ���� !������ ���� ��� ��� ��� ��� ���� �� !5��� �" �� ���� � ����� ��!� �� ������# �� ����� �� �� ���� # ��� � 2�

�� ��� �� �� ������ 1 ��� �� ����# � ��� 2� ����) �.� ���� ����� � � 2� �� ��� � .�1�� ������� ���� � �� .�0� �!��" �� ���1� 1

���+��/� � �!5 .�� ���� ��1 ��������� �"

�� ��&�� ��� ������ ������ ���� !������� �4��� � .� � ���������� � � �"�"�" 7�1�!�� � ���� 9�� �� � � ���� �� 1 �� (��) ������

� ������ " �� �� (��) ������ ���� ���� � � ����� � ���������!�� ����� �� � � � ������ ��� � �� ���� � �� ���������!��

��� ��� ���� ���+����" ���� /�� � ����� ��� �� �&��� � � ����� � ����� � ������� 1 &� � ��&� �� � � ���� . ��� ������ ����

!������� �4���"

�� � ��������� 7�1�!�� . ��������� ���� �����4� ��� 1 ������ 2� .�� ������&���� � 2� �� ��&�� ��� �� ��) ��������� �

� ���������� � �� ��&� �� !������" �� ��� ���� � � �����# ���� ��� �# �� ��� � .� ���1��� 1 ��������� �� ����� ���� � ��� ��������

Page 11: Algoritmos divide y vencerás para la resolución de sistemas lineales tridiagonales ... · 2016. 8. 20. · Algoritmos divide y vencerás para la resolución de sistemas lineales

1 ��� � ����� � ��� 2� . ����������� ���� !������� �4���" (� &� � ����� � �� � ��� ����!5�# ��� ��� � ����! � 1 �����4� �� � ��

.�� &������ � �4���" �� ��� ��� ����� � 0� � ����� �� �� " ! � . ������� � ��) ���� ������� � 1 �� ��� � .� � �������� ��

������� 1 � � �������" � �� � ) ���� ������ � � �� 4�� �� ��&�� � � �� ����� � � � ����" ����� ��� �����4� ��� � .�� �1�����

���.� � ��� ��&�� ����� ��� �� �� )� ���� �!5" -�� �� � ������ � ��� � ����� 2� �� � ������� �� ��� �� ��������� �# ���

� ����� � 1 �� � �������/���!��" �� ���!5� ����� � : ���# � �� 2� 2�� �� ����� � � �� ��������� � ���&�0� 1# ��� ����� � ����# ��

������� 2� � � �� ���� �!5� � �!5�"

��� � ������ ���&�0�� ������� � � ��� � ������!�� ��� �!����� 1 � ������!5� � �� �� 4���/� � ��� ��� �!������" ��� ��)� �

��������/ 1 ������� ����!5�" ������ . ��� ���������� ���!�� ����� )��0 1 �� . ��� ������ &� � 0�����" �� ������� � ��1 ���������

���� �!5"

���� � ����� .� ���� ��&) �������� ��� � ���1 ��� � ��) �������!�� �!�� �� �:';�<'== � �� ��� ���!�� � � ��� � ��� 4���/�

��� ���� ��) �������!�� �� ��!5+��"

Page 12: Algoritmos divide y vencerás para la resolución de sistemas lineales tridiagonales ... · 2016. 8. 20. · Algoritmos divide y vencerás para la resolución de sistemas lineales

�������

��� �� ��� ����

��� �� ����� ���

�������� ����

��� ����� � ��� �������

$"$ �� ������� � " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $

$"> ��������� � � ���� ��)�� 1 ) �� �!�� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " =

$"? �! ����� � � ������!�� � ���� ��� ��� �� � ����������� � " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $>

$"?"$ �! ����� ���� �������� ���� ���� ��� ����������� � " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $?

Page 13: Algoritmos divide y vencerás para la resolución de sistemas lineales tridiagonales ... · 2016. 8. 20. · Algoritmos divide y vencerás para la resolución de sistemas lineales

�� �������

$"?"> �! ���� � � �������� ������� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $@

$"?"? �! ���� � � �����!�� �!5����� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $'

$"% �! ����� ���� �������� ���� �������� �� ��) ��� � ��� �����/ " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " >=

$"@ :� ) ������� � ���������� � � ��� ��� ��� ����������� � " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " >;

! "� ������ ��� #

>"$ :� ) ����������!�� � �� ���������!�� ����� �� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " ?$

>"> �� ��� �� � ���������!�� :�� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " ?@

>"? �� ��� �� � ����������!�� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " ?'

>"% �� ��� �� � ���� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " %<

>"@ 9���� � � �# � 1 � � ��������� �!�2����� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " %>

# ����� ��� ������ � ������� ����� �� � $������ �� �%����&'������� ()

?"$ ����������!�� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " %=

?"> (� ��������� � �����)� ���� ���� ��� ����������� � " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " %'

?"? (� ��������� :�� � ���� ������ " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " A@

Page 14: Algoritmos divide y vencerás para la resolución de sistemas lineales tridiagonales ... · 2016. 8. 20. · Algoritmos divide y vencerás para la resolución de sistemas lineales

������� ���

?"?"$ � �������!�� � � ��������� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " A@

?"?"> ���� ������������� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " =?

?"% (� ��������� :�� &����� � � �! ���� �������� ������� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " =;

?"%"$ � �������!�� � � ��������� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " =;

?"%"> ���� ������������� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " ;>

?"@ � �������� � !������ 1 ����������� � " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " ;?

?"@"$ �� ���� � �� �:� ��> " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " ;?

?"@"> �� ���� � �� ��B �?� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " ;;

?"@"? �� ���� � �� ����� � � � ������ " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " '$

?"@"% ������� � � ����� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " '?

( '�� ���� ������ � �������� ����� �� � $������ �� �%����&'�������&*������� +

%"$ ����������!�� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $<$

%"> (� ��������� � � ��� � � ���� ���� �������� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $<%

%">"$ � �������!�� � � �! ���� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $<%

%">"> ���� ������������� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $$=

Page 15: Algoritmos divide y vencerás para la resolución de sistemas lineales tridiagonales ... · 2016. 8. 20. · Algoritmos divide y vencerás para la resolución de sistemas lineales

�� �������

%"? (� ��������� :�� � � ���� ���� �������� � � ��� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $$;

%"?"$ � �������!�� � � �! ���� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $$;

%"?"> ���� ������������� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $>$

%"% ��������� :�� ���� �������� �����/���� � �! ���� �������� ������� " " " " " " " " " " " " " " " " " " " " " " " " " " " $>?

%"%"$ � �������!�� � � �! ���� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $>%

%"%"> ���� ������������� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $?>

%"@ �������� :�� ���� �������� &����� � � �! ���� � � �����!�� �!5����� " " " " " " " " " " " " " " " " " " " " " " " " " " $?;

%"@"$ � �������!�� � � �! ���� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $?;

%"@"> ���� ������������� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $%?

%"A � �������� � !������ 1 ����������� � " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $%A

%"A"$ �� ���� � �� �:� ��> " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $%=

%"A"> �� ���� � �� ��B �?� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $%;

%"A"? �� ���� � �� ����� � � � ������ " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $@%

%"A"% ������� � � �� ��� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $@%

, '�� ��� ������ � �������� �� ������� -#

Page 16: Algoritmos divide y vencerás para la resolución de sistemas lineales tridiagonales ... · 2016. 8. 20. · Algoritmos divide y vencerás para la resolución de sistemas lineales

������� �

@"$ ����������!�� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $A?

@"> � �������!�� � � �! ���� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $AA

@"? ��������� :�� ��)�� 1 ) �� �!�� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $=A

@"?"$ �������� :�� &����� � � �! ���� � :��� �� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $=A

@"?"> ���� ������������� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $;<

@"?"? �������� :�� ����+���� &����� � � �! ���� � :��� �� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $;>

@"?"% ���� ������������� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $;@

@"?"@ �������� :�� �����/���� � �! ���� �������� ������� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $;=

@"?"A ���� ������������� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $'$

@"% � �������� � !������ 1 ����������� � " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $'?

@"%"$ �� ���� � �� �:� ��> " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $'?

@"%"> �� ���� � �� ��B �?� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $'A

@"%"? �� ���� � �� ����� � � � ������ " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $''

@"%"% ������� � � �� ��� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " ><>

- "� ���� ����� ��� �� ��� ����� ��� !+.

Page 17: Algoritmos divide y vencerás para la resolución de sistemas lineales tridiagonales ... · 2016. 8. 20. · Algoritmos divide y vencerás para la resolución de sistemas lineales

�� �������

A"$ ��������� ���� �������� � � �:� ��> " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " ><'

A"> ��������� ���� �������� � � ��B �?� " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " >$'

A"? ��������� ���� �������� � �� ����� � � � ������ " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " >>A

������������ � ��/��� $� ��� �� ��0� !#

��������$�/ !#,

Page 18: Algoritmos divide y vencerás para la resolución de sistemas lineales tridiagonales ... · 2016. 8. 20. · Algoritmos divide y vencerás para la resolución de sistemas lineales

������� �� 1���

>"$ 9���� � � ��� ���!�� ���� �# �# � 1 ����" " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " %%

?"$ �� ���� � !������ ���� ��� ���������� ?"?# ?"% 1 ?"@ � ����� � �� �:� ��> ������ ��� �� �C���. � ���� � ����� ��� 1

��� 3�!�� �. �� �" " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " ;%

?"> �� � ����� � �� ���� ��� ��� ���������� ?"% 1 ?"@# � ����� � ���� ���0 �" " " " " " " " " " " " " " " " " " " " " " " " " " ;A

?"? �� ���� � !������ ���� ��� ���������� ?"?# ?"% 1 ?"@ � ����� � �� ��B �?� ���� ># %# ;# $A# ?># A%# $>; 1 >@A ���� ����� �" ;;

?"% 8!�� �� !������ � ���� ����� � 1 �� � ����� � �� ���� ���� �� 0 ����!�� � ��� ���������� ?"% 1 ?"@ � �� ��B �?�" '<

?"@ �� ���� � !������ 1 �� � ����� � �� ���� ���� ��� ���������� ?"?# ?"% 1 ?"@ � �� ����� � � � ������" " " " " " " " " " " " '>

?"A �� ��� 1 +�� ���� � ��� ���������� ?"?# ?"% 1 ?"@ ���� � D ><'=$@>" " " " " " " " " " " " " " " " " " " " " " " " " " " " " " '%

%"$ �� ���� � !������ ���� ��� ���������� %"># %"?# %"% 1 %"@ � �� �:� ��> ��� �C���." " " " " " " " " " " " " " " " " " " " " " " $%=

���

Page 19: Algoritmos divide y vencerás para la resolución de sistemas lineales tridiagonales ... · 2016. 8. 20. · Algoritmos divide y vencerás para la resolución de sistemas lineales

���� ����� � �����

%"> �� ���� � !������ ���� ��� ���������� %"># %"?# %"% 1 %"@ � �� �:� ��> ��� �. �� �" " " " " " " " " " " " " " " " " " " " " " $%'

%"? �� ���� � !������ ���� ��� ���������� %"># %"?# %"% 1 %"@ � �� ��B �?� � �� � D ><%; .���� � D A@@?A" " " " " " " " " $@<

%"% �� ���� � !������ ���� ��� ���������� %"># %"?# %"% 1 %"@ � �� ��B �?� � �� � D $?$<=> .���� � D %$'%?<%" " " " " " " $@$

%"@ 8!�� �� !������ � ���� ����� � � �� ��B �?� ���� )���� � � � ����� ������ ��� � D ><%; 1 � D %$'%?<%" " " " " " $@?

%"A �� ���� � !������ ���� ��� ���������� %"># %"?# %"% 1 %"@ � �� ����� � � � ������" " " " " " " " " " " " " " " " " " " " " " " $@@

%"= �� ��� 1 +�� ���� � � ��������� ��" %"> ���� ��� �����/ � ����4�� � D ><'=$@>" " " " " " " " " " " " " " " " " " " " " " $@=

@"$ �� ���� � !������ ���� ��� ���������� @"$# @"> 1 @"? � ����� � �� �:� ��> ������ ��� �� �C���. � ���� � ����� ���" " " $'%

@"> �� ���� � !������ ���� ��� ���������� @"$# @"> 1 @"? � ����� � �� �:� ��> �����/���� ��� 3�!�� �. �� �" " " " " " " " " " $'@

@"? �� ���� � !������ ���� ��� ���������� @"$# @"> 1 @"? � ����� � �� ��B �?� �����/���� ># %# ; 1 $A ���� ����� �" " " " " $'=

@"% �� ���� � !������ ���� ��� ���������� @"$# @"> 1 @"? � ����� � �� ��B �?� ���� ?># A%# $>; 1 >@A ���� ����� �" " " " " $';

@"@ 8!�� �� !������ � ���� ����� � � �� ��B �?� ���� ����4��� � ������ � ����� ������ ��� � D ><%; 1 � D %$'%?<%"><<

@"A �� ���� � !������ ���� ��� ���������� @"$# @"> 1 @"? � ����� � �� ����� � � � ������ ���� ># % 1 ; ���� ����� �" " " " " ><$

@"= �� ��� 1 +�� ���� � ��� ���������� @"$# @"> 1 @"? ���� � D ><'=$@>" " " " " " " " " " " " " " " " " " " " " " " " " " " " " " ><?

Page 20: Algoritmos divide y vencerás para la resolución de sistemas lineales tridiagonales ... · 2016. 8. 20. · Algoritmos divide y vencerás para la resolución de sistemas lineales

������� �� 2�����

>"$ �������� ������ ���� �� ���� � ��.� �!�� ���" " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " ?%

?"$ ��������/���!�� 1 �������/���!�� � � ��������� ?"> ���� � 0 ���� ?">" " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " A>

?"> ��2� �� � � ��������� ?"% ���� � D ?> 1 � D %" " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " =<

?"? ��������/���!�� 1 �������/����� � 2� � ���/� � ���� ����� �� ������ 0 ���� � ��������� ?"% ���� � 0 ���� ?">" " " " " " " =>

?"% ��2� �� � � ��������� ?"% ���� � ���� � D ?> 1 � D %" " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " ;<

?"@ 9���� � � � ����� � �� �:� ��> " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " 'A

?"A 9���� � � � ����� � �� ��B 1 �� ����� � � � ������ " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " '=

?"= 9���� � � �� +�� ���� � �� �:� ��> " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " ';

?"; 9���� � � � ����� � �� ��B 1 �� ����� � � � ������ " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " ''

��

Page 21: Algoritmos divide y vencerás para la resolución de sistemas lineales tridiagonales ... · 2016. 8. 20. · Algoritmos divide y vencerás para la resolución de sistemas lineales

� ����� � �������

%"$ ��2� �� � 0 ����!�� � � ��������� %"># ���� % ���� ����� �" " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $><

%"> ��2� �� � ������������ � � � �! ���� ��)�� 1 ) �� �!�� &����� � � �! ���� � �����) ���&����# ���� � D $A" " " " " " " $>=

%"? ��2� �� � 0 ����!�� � � ��������� %"%# ���� ; ���� ����� �" " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $??

%"% ��2� �� � 0 ����!�� � � ��������� E%"@F# ���� ; ���� ����� �" " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $%$

%"@ 9���� � � � ����� � �� �:� ��> " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $@;

%"A 9���� � � � ����� � �� ��B �?� 1 �� ����� � � � ������ " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $@'

%"= 9���� � � �� +�� ���� � �� �:� ��> " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $A<

%"; 9���� � � �� +�� ���� � �� ��B �?� 1 �� ����� � � � ������ " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $A$

@"$ ��2� �� � 0 ����!�� � � ��������� @"$# ���� % ���� ����� �" " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $='

@"> ��2� �� � 0 ����!�� � � ��������� @"># ���� % ���� ����� �" " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " $;%

@"? 9���� � � � ����� � �� �:� ��> " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " ><%

@"% 9���� � � � ����� � �� ��B �?� 1 �� ����� � � � ������ " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " ><@

@"@ 9���� � � �� +�� ���� � �� �:� ��> " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " ><A

@"A 9���� � � �� +�� ���� � �� ��B �?� 1 �� ����� � � � ������ " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " ><=

Page 22: Algoritmos divide y vencerás para la resolución de sistemas lineales tridiagonales ... · 2016. 8. 20. · Algoritmos divide y vencerás para la resolución de sistemas lineales

����� � ������� ��

A"$ �� ���� � �� �:� ��> ��� �C���. ���� � D @$># � D $<>%# � D ><%; 1 � D %<'A " " " " " " " " " " " " " " " " " " " " " " >$$

A"> �� ���� � �� �:� ��> ��� �C���. ���� � D ;$'># � D $A?;%# � D ?>=A; 1 � D A@@?A " " " " " " " " " " " " " " " " " " " >$>

A"? �� ���� � �� �:� ��> ��� �C���. ���� � D ;$'># � D $A?;%# � D ?>=A; 1 � D A@@?A " " " " " " " " " " " " " " " " " " " >$?

A"% �� ���� � �� �:� ��> ��� �C���. ���� � D ><'=$@> 1 � D %$'%?<% " " " " " " " " " " " " " " " " " " " " " " " " " " " " " >$%

A"@ �� ���� � �� �:� ��> ��� �. �� � ���� � D @$># � D $<>%# � D ><%; 1 � D %<'A " " " " " " " " " " " " " " " " " " " " " >$@

A"A �� ���� � �� �:� ��> ��� �. �� � ���� � D ;$'># � D $A?;%# � D ?>=A; 1 � D A@@?A " " " " " " " " " " " " " " " " " " >$A

A"= �� ���� � �� �:� ��> ��� �. �� � ���� � D $?$<=># � D >A>$%%# � D @>%>;; 1 � D $<%;@=A " " " " " " " " " " " " " " >$=

A"; �� ���� � �� �:� ��> ��� �. �� � ���� � D ><'=$@> 1 � D %$'%?<% " " " " " " " " " " " " " " " " " " " " " " " " " " " >$;

A"' �� ���� � �� ��B �?� ���� � D ><%; 1 � D %<'A" " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " >><

A"$< �� ���� � �� ��B �?� ���� � D ;$'> 1 � D $A?;%" " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " >>$

A"$$ �� ���� � �� ��B �?� ���� � D ?>=A; 1 � D A@@?A" " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " >>>

A"$> �� ���� � �� ��B �?� ���� � D $?$<=> 1 � D >A>$%%" " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " >>?

A"$? �� ���� � �� ��B �?� ���� � D @>%>;; 1 � D $<%;@=A" " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " >>%

A"$% �� ���� � �� ��B �?� ���� � D ><'=$@> 1 %$'%?<%" " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " >>@

A"$@ �� ���� � �� ����� � � � ������ ���� � D @$># � D $<>%# � D ><%; 1 � D %<'A " " " " " " " " " " " " " " " " " " " " " " >>=

Page 23: Algoritmos divide y vencerás para la resolución de sistemas lineales tridiagonales ... · 2016. 8. 20. · Algoritmos divide y vencerás para la resolución de sistemas lineales

��� ����� � �������

A"$A �� ���� � �� ����� � � � ������ ���� � D ;$'># � D $A?;%# � D ?>=A; 1 � D A@@?A " " " " " " " " " " " " " " " " " " " " >>;

A"$= �� ���� � �� ����� � � � ������ ���� � D ;$'># � D $A?;%# � D ?>=A; 1 � D A@@?A " " " " " " " " " " " " " " " " " " " " >>'

A"$; �� ���� � �� ����� � � � ������ ���� � D ><'=$@> 1 � D %$'%?<% " " " " " " " " " " " " " " " " " " " " " " " " " " " " " >?<