These exceptions can occur only when the overdetermined system contains enough linearly dependent equations that the number of independent equations does not exceed the number of unknowns.
12.
Beginning from his first works in 1971 3, Dr . Abrosimov studied overdetermined systems of partial differential equations where he successfully applied an original approach developed.
13.
However, an overdetermined system will have solutions in some cases, for example if some equation occurs several times in the system, or if some equations are linear combinations of the others.
14.
For " N " > " J ", orthogonal projection yields the standard overdetermined system of equations ( often called normal equations ) used to compute the coefficients in the polynomial approximation.
15.
He later worked on pseudogroups and their deformation theory, based on a fresh approach to overdetermined systems of PDEs ( bypassing the Cartan-K�hler ideas based on differential forms by making an intensive use of jets ).
16.
In the case of the systems of polynomial equations, it may happen that an overdetermined system has a solution, but that no one equation is a consequence of the others and that, when removing any equation, the new system has more solutions.
17.
Noting that the " n " equations in the " m " variables in our data comprise an overdetermined system with one unknown and " n " equations, we may choose to estimate " k " using least squares.
18.
For a system of linear equations, the number of equations in an indeterminate system could be the same as the number of unknowns, less than the number of unknowns ( an underdetermined system ), or greater than the number of unknowns ( an overdetermined system ).
19.
:: : : : The historical authors of overdetermined system seem to be very sure about it-- its definition has been there since inception on 20 March 2007, and the section " An example in two dimensions " has covered it at great graphical length ever since 15 : 51, 30 May 2007 . talk ) 22 : 17, 29 November 2012 ( UTC)
