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

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

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...

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...

discussed by Abell and Chaffee. When n is greater than four, this system is overdetermined and a fitting method must be used. The amount of error in the results...

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

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...

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

(which implies 5 = 6). Both types of equation system, inconsistent and consistent, can be any of overdetermined (having more equations than unknowns), underdetermined...

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...

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...

that a system of equations, which is not overdetermined and which cannot be reduced to an overdetermined system by using the above-mentioned algebraic property...

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...

Brunelle JA, Moran RF, Data processing in CO-oximeters that Use overdetermined systems (Reply). Clin Chem, 43:1, 189–191, 1997 Degen BR, Moran RF, Comparison...

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

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...

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

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

{\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...

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...

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

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...