@Joe Riel what's wrong?

is (%)=

is(%)=

applyop(`-`, 1, (R1/r0-1)^2)=

is(%)=

@Joe Riel what's wrong?

is (%)=

is(%)=

applyop(`-`, 1, (R1/r0-1)^2)=

is(%)=

How to achieve exactly the expression:

taking into account the signs

GRACIAS

How to achieve exactly the expression:

taking into account the signs

GRACIAS

 Thanks for your support  @pagan ,

In N, there are 18 equations. What was the selection criterion for the set [1, 17, 18, 4, 5, 6, 7, 8, 9, 10, 16, 12]?
Gracias

 Thanks for your support  @pagan ,

In N, there are 18 equations. What was the selection criterion for the set [1, 17, 18, 4, 5, 6, 7, 8, 9, 10, 16, 12]?
Gracias

Why results are so different from those obtained with solve?. To solve the results are similar to those expected.
As you can see the end of the worksheet attached

fsolve(N[1 .. 12], {Zeta1, Zeta2, Zeta3, Zeta4, Zeta5, Zeta6, lambda1, lambda2, lambda3, R0 = 10.0, a = -0.1e-3, b = 0.1e-3});

{R0 = -50.58199437, a = 8.227786623, b = 1.396186420, Zeta1 = 10.09705600, Zeta2 = 0.01000000000, Zeta3 = 19.10950601, Zeta4 = 231.9280000, Zeta5 = 25.93439900, Zeta6 = 419.5270000, lambda1 = 0., lambda2 = 0., lambda3 = 0.}

solve(N, {R0, a, b, Zeta1, Zeta2, Zeta3, Zeta4, Zeta5, Zeta6, lambda1, lambda2, lambda3});

{R0 = 10.09705605, a = -0.0002187538892, b = -0.00002570166028, Zeta1 = 10.09705600, Zeta2 =0.01000000000,  Zeta3 = 19.10950601, Zeta4 = 231.9280000, Zeta5 = 25.93439900, Zeta6 = 419.5270000, lambda1 = 0., lambda2 = 0., lambda3 = 0.},

{ R0 = -3.929320206 10E5 , a = -38923.01649, b = -38923.01629, Zeta1 = 10.09705600, Zeta2 = 0.01000000000,  Zeta3 = 19.10950601, Zeta4 = 231.9280000, Zeta5 = 25.93439900, Zeta6 = 419.5270000, lambda1 = 0., lambda2 = 0., lambda3 = 0. }
                                                             Gracias

Why results are so different from those obtained with solve?. To solve the results are similar to those expected.
As you can see the end of the worksheet attached

fsolve(N[1 .. 12], {Zeta1, Zeta2, Zeta3, Zeta4, Zeta5, Zeta6, lambda1, lambda2, lambda3, R0 = 10.0, a = -0.1e-3, b = 0.1e-3});

{R0 = -50.58199437, a = 8.227786623, b = 1.396186420, Zeta1 = 10.09705600, Zeta2 = 0.01000000000, Zeta3 = 19.10950601, Zeta4 = 231.9280000, Zeta5 = 25.93439900, Zeta6 = 419.5270000, lambda1 = 0., lambda2 = 0., lambda3 = 0.}

solve(N, {R0, a, b, Zeta1, Zeta2, Zeta3, Zeta4, Zeta5, Zeta6, lambda1, lambda2, lambda3});

{R0 = 10.09705605, a = -0.0002187538892, b = -0.00002570166028, Zeta1 = 10.09705600, Zeta2 =0.01000000000,  Zeta3 = 19.10950601, Zeta4 = 231.9280000, Zeta5 = 25.93439900, Zeta6 = 419.5270000, lambda1 = 0., lambda2 = 0., lambda3 = 0.},

{ R0 = -3.929320206 10E5 , a = -38923.01649, b = -38923.01629, Zeta1 = 10.09705600, Zeta2 = 0.01000000000,  Zeta3 = 19.10950601, Zeta4 = 231.9280000, Zeta5 = 25.93439900, Zeta6 = 419.5270000, lambda1 = 0., lambda2 = 0., lambda3 = 0. }
                                                             Gracias

@Robert Israel 

> data := [A = 0.400e-2, B = -0.600e-6, C = 0, W = 2.6];

> T-(W-1)/(A+B*T+C*T^2);

eval(%, data)
             
> Roots(%, T = fdiff(%), T, T = 0), method = modifiednewton, tolerance = 10^(-6), output = information);

   [n      p[n]                   relative error ]
   [                                                   ]
   [0  0.9400000000                  -        ]
   [                                                   ]
   [1  429.0216769       0.9978089685  ]
   [                                                   ]
   [2  427.4007353    0.003792556882 ]
   [                                                   ]
   [                                                -8]
   [3  427.4007043   7.253146681 10   ]

The initial intention was to get, with the help of maple, up from the initial equation to the equation recurrence. Designing statement algebraically. Finding the recurrence relation ..Solving Recurrence Relations. Help me  in this, pleas
Gracias

@Robert Israel 

> data := [A = 0.400e-2, B = -0.600e-6, C = 0, W = 2.6];

> T-(W-1)/(A+B*T+C*T^2);

eval(%, data)
             
> Roots(%, T = fdiff(%), T, T = 0), method = modifiednewton, tolerance = 10^(-6), output = information);

   [n      p[n]                   relative error ]
   [                                                   ]
   [0  0.9400000000                  -        ]
   [                                                   ]
   [1  429.0216769       0.9978089685  ]
   [                                                   ]
   [2  427.4007353    0.003792556882 ]
   [                                                   ]
   [                                                -8]
   [3  427.4007043   7.253146681 10   ]

The initial intention was to get, with the help of maple, up from the initial equation to the equation recurrence. Designing statement algebraically. Finding the recurrence relation ..Solving Recurrence Relations. Help me  in this, pleas
Gracias

So I made in Excel.
How easily do in maple?
How to arrive at the recursive function?

RecurrenceEquationSo.xls

So I made in Excel.
How easily do in maple?
How to arrive at the recursive function?

RecurrenceEquationSo.xls

@acer 

My apologies, I was just translating the source from which I tried to reproduce the theory. I do need an explanation of SVD. For me it is something new, I intuitively, I think I can be of great benefit. Except that most of the examples and theory to which I have had access is for compaction of images and LSI. Right now I'm trying  understand, Total Least Squares with SVD. In the attached document I have some doubts.
If the values of U and V are unit values, how the singular vector corresponding to smaller singular value, will my coefficients. I tried to implement this without the graphical results.
If you have an array of uncertainties for the X and others to the Y, how to implement the matrix A and B for the algorithm that can be seen on Wikipedia

Fitting_Least_Square.mw

@acer 

My apologies, I was just translating the source from which I tried to reproduce the theory. I do need an explanation of SVD. For me it is something new, I intuitively, I think I can be of great benefit. Except that most of the examples and theory to which I have had access is for compaction of images and LSI. Right now I'm trying  understand, Total Least Squares with SVD. In the attached document I have some doubts.
If the values of U and V are unit values, how the singular vector corresponding to smaller singular value, will my coefficients. I tried to implement this without the graphical results.
If you have an array of uncertainties for the X and others to the Y, how to implement the matrix A and B for the algorithm that can be seen on Wikipedia

Fitting_Least_Square.mw

@acer 

The document in the link explains how to use SVD. It's just a method to factor a matrix A into a product of three matrices A = USV^T where U and V are orthogonal matrices and S is diagonal. It is useful in solving the least squares normal equation A^TAx= A^Tb for x by avoiding the matrix multiplications of A^TA and A^Tb. The steps are listed in the document. In the end, you can solve for x as follows:

x = VS^-1U^Tb

The formula we use was not found in the documents I consulted in the use of SVD for least squares adjustments. I'd like guidance on this issue with some link where I can read about it. Or please to tell me something about it
Thank you very much for your response.