= Trial function
A trial function is a chosen candidate used to approximate a solution or evaluate a <variational principle>. For an <eigenvalue> upper bound from a <Rayleigh quotient>, it must be nonzero, have finite numerator and denominator, and lie in the appropriate variational domain. In a <Dirichlet problem> it satisfies the fixed endpoint values. Natural boundary conditions need not always be imposed on a trial in the quadratic-form domain, but a candidate violating an essential <boundary condition> does not give the stated bound.
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