mathematics, a system of equations is considered overdetermined if there are more equations than unknowns.[citation needed] An overdetermined system is almost...

Overdetermined may refer to: Overdetermined systems in various branches of mathematics Overdetermination in various fields of psychology or analytical...

this sense, the algorithm is also an effective method for solving overdetermined systems of equations. It has the advantage that second derivatives, which...

underdetermined if there are fewer equations than unknowns (in contrast to an overdetermined system, where there are more equations than unknowns). The terminology...

a system of linear differential equations is said to be overdetermined if there are more equations than the unknowns. For an overdetermined system to...

restricting to one-dimensional motion) a spring system can be cast as a (possibly overdetermined) system of linear equations or equivalently as an energy...

overdetermined systems, when constructed with random coefficients, are inconsistent. For example, the system x3 – 1 = 0, x2 – 1 = 0 is overdetermined...

more equations than unknowns has no solution. Such a system is also known as an overdetermined system. In the first case, the dimension of the solution set...

Adjustment of observations, in mathematics, a method of solving an overdetermined system of equations Calibration, in metrology Spinal adjustment, in chiropractic...

conditions for finding a maximal set of independent solutions of an overdetermined system of first-order homogeneous linear partial differential equations...

hesse normal forms of the corresponding lines. The solution of this overdetermined system found by the least squares method gives the coordinates of the point...

parameters ( β {\displaystyle {\boldsymbol {\beta }}} ). Consider an overdetermined system ∑ j = 1 p x i j β j = y i ,   ( i = 1 , 2 , … , n ) , {\displaystyle...

(an overdetermined system). Conversely, any of those three cases may or may not be indeterminate. The following examples of indeterminate systems of equations...

are the multiplicities of the distinct roots. This equation is an overdetermined system for having k {\displaystyle k} variables z 1 , … , z k {\displaystyle...

QS, Q orthogonal, S symmetric positive-semidefinite Consider an overdetermined system of linear equations, as might occur with repeated measurements of...

if there are any. A system with a higher number of equations than variables is called overdetermined. If an overdetermined system has any solutions, necessarily...

{\displaystyle {\sqrt {a^{2}-b^{2}c}}} is a rational number. Consider this overdetermined system of equations (with 3 equations in just 2 unknowns): x − 2 y + 1...

Least-squares adjustment is a model for the solution of an overdetermined system of equations based on the principle of least squares of observation residuals...

squares: see below. Least squares is the standard method used with overdetermined systems. Squaring is used in statistics and probability theory in determining...

linear least squares is the problem of approximately solving an overdetermined system of linear equations A x = b, where b is not an element of the column...

Since the n equations in the m variables in our data comprise an overdetermined system with one unknown and n equations, we estimate k using least squares...

instead the Lax equation arises as a consistency equation for an overdetermined system. The Lax pair ( L , P ) {\displaystyle (L,P)} can be used to define...

for magnitude and another 128 for the phase). This is a massively overdetermined system, meaning that the number of equations is much larger than the number...

the theory of several complex variables. They form a significant overdetermined system of PDEs. This is done using a straightforward generalization of...

to create many more than the minimal required set (creating an overdetermined system), and use least squares regression to derive a set of function parameters...

comparisons may be false because of round-off errors). If the system is overdetermined – so that A has more rows than columns – the pseudoinverse A+ (in...

pairs. This will result in an overdetermined system with multiple solutions. To get estimates for an overdetermined system, least squares can be used. The...

{\displaystyle \beta _{i}} have been collected, the problem reduces to an overdetermined system of N {\displaystyle N} non-linear equations. The state vector associated...

pseudogroups and their deformation theory, based on a fresh approach to overdetermined systems of PDEs (bypassing the Cartan–Kähler ideas based on differential...

factorization yields an overdetermined system of equations in the coordinates of the vector x: subject to the constraint This system admits the solutions...