zagatov wrote:
i have an equation system which is

f (x1,x2)=(x1-c)^2 + (x2-c)^2 - c
f (x1,x3)=(x1-c)^2 + (x2-c)^2 - c
f (x1,x4)=(x2-c)^2 + (x2-c)^2 - c
f (x1,x5)=(x2-c)^2 + (x2-c)^2 - c
,
,
can go on

it is roughly depicted

It is so "roughly depicted " as to be meaningless

but i can say that generally
c's are different constants and i have 2 variable and   more than 2
or
3 equations.
Aim is to find minimal amount of residual for all f functions.
i tried to use some gradient methods but numbers of variables must be
equal to
numbers of equations. than i stucked. i want to use steepest descent
or newtonian methods.

How can i prove this?
help me it is so crucial
please at least tell me what to read about or point me where the
solution is.

There seems nothing "statistical" here. You seem to have one variable for each equation, so notionally you can just solve each equation separately (provided it has at least one root).

If you need help, I suggest you set out your problem far better than you have managed above.

David Jones

i have an equation system which is

f (x1,x2)=(x1-c)^2 + (x2-c)^2 - c
f (x1,x3)=(x1-c)^2 + (x2-c)^2 - c
f (x1,x4)=(x2-c)^2 + (x2-c)^2 - c
f (x1,x5)=(x2-c)^2 + (x2-c)^2 - c
,
,
can go on


it is roughly depicted

but i can say that generally
c's are different constants and i have 2 variable and more than 2
or
3 equations.
Aim is to find minimal amount of residual for all f functions.
i tried to use some gradient methods but numbers of variables must be
equal to
numbers of equations. than i stucked. i want to use steepest descent
or newtonian methods.


How can i prove this?
help me it is so crucial
please at least tell me what to read about or point me where the
solution is.

On 6 Mart, 12:40, "David Jones" <dajx...@ceh.ac.uk> wrote:
zagatov wrote:
i have an equation system which is

f (x1,x2)=(x1-c)^2 + (x2-c)^2 - c
f (x1,x3)=(x1-c)^2 + (x2-c)^2 - c
f (x1,x4)=(x2-c)^2 + (x2-c)^2 - c
f (x1,x5)=(x2-c)^2 + (x2-c)^2 - c
,
,
can go on

it is roughly depicted

It is so "roughly depicted " as to be meaningless

but i can say that generally
c's are different constants and i have 2 variable and more than 2
or
3 equations.
Aim is to find minimal amount of residual for all f functions.
i tried to use some gradient methods but numbers of variables must
be equal to
numbers of equations. than i stucked. i want to use steepest descent
or newtonian methods.

How can i prove this?
help me it is so crucial
please at least tell me what to read about or point me where the
solution is.

There seems nothing "statistical" here. You seem to have one
variable for each equation, so notionally you can just solve each
equation separately (provided it has at least one root).

If you need help, I suggest you set out your problem far better than
you have managed above.

David Jones

i study multidimensional scaling, i first tried Iterative Majorization
to converge the points to real distance,
than i need to try kruskal-shepard methods to converge the points , i
know both newton and steepest descent
my knowledge about linear algebra may be lower than avarage but when i
will calculate the inverse of jacobian matrices
numbers of functions exceed numbers of variables so i couldnt find the
inverse of jacobian.
so i need help , exact solution.