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This reduces the satisfiability and validity problems to the problem of solving a parity game.
This turns the reconstruction into the problem of solving a homogeneous system of algebraic linear equations.
The problem of solving a linear system of equations is widely encountered in many fields of science and engineering.
Such a problem reduces to the problem of solving a large tridiagonal system of linear equations with an almost Toeplitz structure.
We let P i) denote the problem of solving a discrete Poisson equation on a (2^i+1 -by-(2^i+1 -by-d, with (2^i+1)^2 unknowns.
By applying a model predictive control (MPC) method, we formulate the problem of finding the optimal joint train regulation and passenger flow control strategy as the problem of solving a set of quadratic programming (QP) problems, under which an optimal control law can be numerically calculated efficiently using a quadratic programming algorithm.
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By introducing a sensitivity parameter and expanding power series around it, the optimal tracking control problem can be simplified into the problem of solving an infinite sum of linear optimal control series without time-delay and disturbance.
Equation (15) is equivalent to the problem of solving the transcendent equation A sin ( x ) = sin ( B x ), (16).
This paper considers the problem of solving Bayesian decision problems with a mixture of continuous and discrete variables.
In this zetetic stage of analysis, the geometrical problem is transformed into the algebraic problem of solving a standard-form cubic equation (i.e., a cubic equation that does not include a quadratic term).
In this way, the complex problem of solving an over-determined system of quadratic equations is reduced to solve an over-determined system of linear equations.
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