vslesing.dat

basic linear algebra classes and applications (SVD,interpolation, multivariate optimization)

./vslesing


Verify application of SVD to solving sets of simultaneous equations


Checking solution of a set of linear equations
with a Hilb+E of order 10x10

condition number 2.75192
true vs. computed solution follows 

Matrix 1:2x1:10  is not engaged


     |        1  |        2  |        3  |        4  |        5  |        6  |
-------------------------------------------------------------------------------
   1 |          1            2            3            4            5            6  
   2 |          1            2            3            4            5            6  


     |        7  |        8  |        9  |       10  |
-------------------------------------------------------------------------------
   1 |          7            8            9           10  
   2 |          7            8            9           10  
Done
	checking to see that Ax is indeed b
Two (3,1) elements of matrices with values 9.79358 and 9.79358
differ the most, although the deviation 3.8147e-06 is small


Checking solution of a set of linear equations
with a Hilb+E of order 20x10

condition number 2.7952
true vs. computed solution follows 

Matrix 1:2x1:10  is not engaged


     |        1  |        2  |        3  |        4  |        5  |        6  |
-------------------------------------------------------------------------------
   1 |          1            2            3            4            5            6  
   2 |          1            2            3            4            5            6  


     |        7  |        8  |        9  |       10  |
-------------------------------------------------------------------------------
   1 |          7            8            9           10  
   2 |          7            8            9           10  
Done
	checking to see that Ax is indeed b
Two (7,1) elements of matrices with values 11.4156 and 11.4156
differ the most, although the deviation 3.8147e-06 is small


Checking solution of a set of linear equations
with a Hilbert matrix of order 10

condition number 8.94709e+08

SVD solver of AX=B detected a linear dependency among X
  #  singular value	null coefficients
 7      1.2e-07 	(0.00130963 -0.0394396   0.269146  -0.616852   0.308427   0.394039 -0.0290467  -0.351558  -0.257763   0.322839 )
 8      2.6e-09 	(         0 0.00283669 -0.0518273   0.279691  -0.562661   0.245453   0.411889  -0.123976  -0.511031   0.309951 )
 9        2e-09 	(         0 0.000267683 -0.0073021  0.0653878  -0.271881   0.589665   -0.67155    0.34876 -0.0243657 -0.0290013 )
 10      2.4e-09 	(         0 -0.000503957  0.0115796 -0.0849961   0.267981  -0.339047 -0.0717925   0.633468  -0.603703   0.187034 )
true vs. computed solution follows 

Matrix 1:2x1:10  is not engaged


     |        1  |        2  |        3  |        4  |        5  |        6  |
-------------------------------------------------------------------------------
   1 |          1            2            3            4            5            6  
   2 |     0.9995         2.01        2.955        4.055        5.013        5.971  


     |        7  |        8  |        9  |       10  |
-------------------------------------------------------------------------------
   1 |          7            8            9           10  
   2 |      6.975        8.004        9.022        9.996  
Done
	checking to see that Ax is indeed b
Two (5,1) elements of matrices with values 5.32709 and 5.32708
differ the most, although the deviation 9.53674e-07 is small

Compilation finished at Fri Dec 25 23:25:24