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Matrix A :%7.2lf Matrix A^-1 : The approximate relative fault of A and A^-1 is : %.20lf The approximate relative modulo of A and A^-1 is : %.20lf Condition number of A matrix : %lf %10.2lf Matrix A^-1 : Matrix A*A^-1 : Due to the fact that in random matrices we don't know the inverted vector faults are not computed, as you can see, and so alternatively we compute the inverted matrix B=A^-1 and also the multiplication of A*B = A*A^-1 so that we can proove that method Cholesky worked well. We can reach to this conclusion if the printed A*B is the unit matrix(I). Execution of Cholesky method to compute A^-1 matrix ended...Execution time of Cholesky to compute A^-1 : %.4lf ms Execution of Cholesky method for linear system Ax = b resolution started... Matrix A with vector b in last column : Matrix I: Matrix I^-1: Vector y :y =( %7.2lf, %7.2lf )^T LINEAR SYSTEM SOLUTION : x = ( The approximate relative fault of system is : %.20lf The approximate relative modulo of system is : %.20lf Execution of Cholesky method for linear system Ax = b resolution ended...Execution time of Cholesky system : %.4lf ms rask1_Cholesky_2_a.txtFILE ERROR : Either the file with name 'ask1_Cholesky_1_a.txt' does not exist or it is placed in a wrong directory%dDimensions given from the file are %dX%d %lfGive matrix[NXN] dimension N(e.g. 100,500,1000) : Give Pascal matrix[NXN] dimension N (e.g. 100,500,1000) : Specific matrices LIST Switch the specific matrix to solve a linear system as given from exercise ask1_Cholesky.1.a: 1. Matrix of dimensions 4X4 (adjustment 2.a.1) 2. Moler Matrix of dimensions 5X5 (adjustment 2.a.2) 3. Pascal Matrix of dimensions 5X5 (adjustment 2.a.3) 4. Pascal Matrix of dimensions 8X8 (adjustment 2.a.4) 5. Pascal Matrix of dimensions NXN, where N given by you with values 100,500,1000 and system solution: x=(1,1,...,1,1)^T(adjustment 2.a.5) 6. Matrix of dimensions NXN, where N given by you with values 100,500,1000 and system solution: x=(1,1,...,1,1)^T (adjustment 2.a.6) 7. Select if you want to return to MAIN MENU.INPUT: Give vector data below:X[%d] = Give matrix[NXN] dimension N : Insert matrix data below:A[%d][%d] = Give vector b data below:b[%d] = MAIN MENU Switch your method of giving a system: 1. User Input: you are about to insert the A matrix and the b vector directly from keyboard 2. Use specific matrices: you are about to switch from a list of given matrices 3. Use ramdom matrices: you are about to select only the size of the matrix you want and the matrix will be generated randomly 4. File input: you are about to give a text file with your matrices in it. The file name must have the name:'ask1_Cholesky_2_a.txt' 5. Select if you want to quit. sometimes the usage of random shows problems... i haven't fixed that yet... try small numbers!!! in most cases it succeeds!! LINEAR SYSTEM RESOLUTION OF Ax = b SYSTEMS USING CHOLESKY FACTORIZATION METHOD HOPEFULLY I WILL GET SOME TIME IN CRISTMASS TO CHECK SOME FEW ERRORS IN MY CODE ANYWAY, HOPE THAT YOU ENJOYED USING MY PROGRAM FOR SOLVING LINEAR SYSTEMS OF TYPE Ax=B USING THE CHOLESKY FACTORIZATION REGARDS NIKOLAOS BEGETIS UNDERGRADUATE STUDENT OF DEPARTMENT OF INFORMATICS AND TELECOMMUNICATIONS, UNIVERSITY OF ATHENS 2011-2012 hFd{۵&= @@@@@@@B@$@.@5@<@^@4@A@L@U@t@Q@_@@j@@o@|@К@@Ъ@#@7@@@"@@@?@@@;` *~68|\FzP|$  .p  D$  h«  V $  ΰE  i  ~  DE (h޲G 8&    HWe ԅ lho 0  <4oĄoo*:JZjzʆچ *:GCC: (GNU) 4.2.4 (Ubuntu 4.2.4-1ubuntu3)GCC: (GNU) 4.2.4 (Ubuntu 4.2.4-1ubuntu3)GCC: (GNU) 4.2.4 (Ubuntu 4.2.4-1ubuntu4)GCC: (GNU) 4.2.4 (Ubuntu 4.2.4-1ubuntu4)GCC: (GNU) 4.2.4 (Ubuntu 4.2.4-1ubuntu3)GCC: (GNU) 4.2.4 (Ubuntu 4.2.4-1ubuntu4)GCC: (GNU) 4.2.4 (Ubuntu 4.2.4-1ubuntu3)$ԅ"l$!u_IO_stdin_useduttg$ZUi7intPpAOK'/build/buildd/glibc-2.7/build-tree/i386-libc/csu/crti.S/build/buildd/glibc-2.7/build-tree/glibc-2.7/csuGNU AS 2.18.0] /build/buildd/glibc-2.7/build-tree/i386-libc/csu/crtn.S/build/buildd/glibc-2.7/build-tree/glibc-2.7/csuGNU AS 2.18.0% $ > $ > $ > 4: ; I?  &IU%U%# init.cN /build/buildd/glibc-2.7/build-tree/i386-libc/csucrti.Sԅ!/!=Z!gg//l(!/!=Z!xN /build/buildd/glibc-2.7/build-tree/i386-libc/csucrtn.S !!!!!!GNU C 4.2.4 (Ubuntu 4.2.4-1ubuntu3)short unsigned intshort int_IO_stdin_usedlong long unsigned intunsigned char/build/buildd/glibc-2.7/build-tree/glibc-2.7/csuinit.clong long intԅl.symtab.strtab.shstrtab.interp.note.ABI-tag.gnu.hash.dynsym.dynstr.gnu.version.gnu.version_r.rel.dyn.rel.plt.init.text.fini.rodata.eh_frame_hdr.eh_frame.ctors.dtors.jcr.dynamic.got.got.plt.data.bss.comment.debug_aranges.debug_pubnames.debug_info.debug_abbrev.debug_line.debug_str.debug_ranges44#HH 5hh1o  $; 00`CKo,XoĄpg 44p << yԅ0t@PP0ll77FdFHHHHIIX$$J 00J0J&XKPK%KtMo"M).0 O9O@PGW0$8 H^4Hh 0Ą4 < ԅ  P l$0 !,:G ]0l,s @ "$ -i >`Oж _P fVQ {«    ޲G lu 8 Wԇ- e >A$f܍> 2,ȉ G(TZ d9v~ X $  0|ΰE Z !E *.p I4N^  $F  0 $AV Ue: |& ԅ init.cinitfini.ccrtstuff.c__CTOR_LIST____DTOR_LIST____JCR_LIST____do_global_dtors_auxcompleted.5843p.5841frame_dummy__CTOR_END____DTOR_END____FRAME_END____JCR_END____do_global_ctors_auxask1_Cholesky_2_a.cpp_GLOBAL_OFFSET_TABLE___init_array_end__init_array_start_DYNAMICdata_start_Z11userInput_Xisrand@@GLIBC_2.0__libc_csu_fini_start_Z14allocateMatrixii_Z12fileInput_AXPiPPd__gmon_start___Jv_RegisterClasses_fp_hw_Z15MolerMatrix_5X5PiPPd_Z13randomInput_APi_finiputchar@@GLIBC_2.0_Z16PascalMatrix_5X5PiPPd__libc_start_main@@GLIBC_2.0_Z18apprRelativeModuloPPdS_S_i_Z9factoriali_Z16PascalMatrix_8X8PiPPdperror@@GLIBC_2.0_IO_stdin_usedgettimeofday@@GLIBC_2.0free@@GLIBC_2.0scanf@@GLIBC_2.0__data_startsqrt@@GLIBC_2.0fclose@@GLIBC_2.1_Z13randomInput_Xifopen@@GLIBC_2.1_Z17apprRelativeFaultPdS_i__dso_handle__libc_csu_initprintf@@GLIBC_2.0_Z11userInput_APi_Z7maxNormPdi_Z8CholeskyPPdS_i_Z16PascalMatrix_NXNPiPPdtime@@GLIBC_2.0__bss_startmalloc@@GLIBC_2.0_Z21list_specificMatricesv_Z13maxMatrixNormPPdi_Z4menuv_Z17Cholesky_invertedPPdS0_iii_endputs@@GLIBC_2.0_Z28Cholesky_factorizationMethodPPdPS0_S1_i_Z26apprRelativeFault_invertedPPdS0_irand@@GLIBC_2.0fscanf@@GLIBC_2.0_Z27apprRelativeModulo_invertedPPdS0_S0_i_Z19matrix_4X4_CholeskyPiPPd_edata__gxx_personality_v0@@CXXABI_1.3_Z10matrix_NXNPiPPdexit@@GLIBC_2.0__i686.get_pc_thunk.bxmain_init