45 results about "Linear algebraic equation" patented technology

A computer implemented method (200) is described for determining the equivalence of two sets of simultaneous linear algebraic equations. Each of said equations is of a form: ei1x1+ei2x2+ei3x3+ . . . +eiixn=bi wherein xj are unknowns, eij are coefficients and bi are quantities, and defining the relationship between the unknowns within the set. The coefficients and quantities are known algebraic expressions. The unknowns are iteratively eliminated (250 to 280) from each of the sets of simultaneous linear algebraic equations until each of said equations are in the form: (lii)kxi=(ri)k wherein lii and ri are algebraic expressions, and k={1;2} indicate one of said sets that said equation is derived from. The products (lii)1*(ri)2 and (lii)2*(ri)1 are compared (300) for each of the unknowns. Only if the products match (310) for all the unknowns are the two sets of simultaneous linear algebraic equations equivalent (312). An apparatus (100) for performing the above method (200) is also provided.

A computer implemented method (200) is described for determining the equivalence of two sets of simultaneous linear algebraic equations. Each of said equations is of a form:ei1x1+ei2x2+ei3x3+ . . . +eiixn=biwhere xj are unknowns, eij are coefficients and bi are quantities, and defining the relationship between the unknowns within the set. The coefficients and quantities are known algebraic expressions. The unknowns are iteratively eliminated (250 to 280) from each of the sets of simultaneous linear algebraic equations until each of said equations are in the form:(lii)kxi=(ri)kwherein lii and ri are algebraic expressions, and k={1;2} indicate one of said sets that said equation is derived from. The products (lii)1*(ri)2 and (lii)2*(ri)1 are compared (300) for each of the unknowns. Only if the products match (310) for all the unknowns are the two sets of simultaneous linear algebraic equations equivalent (312). An apparatus (100) for performing the above method (200) is also provided.

The invention discloses a linear pseudo-spectrum GNEM guidance and control method. According to the linear pseudo-spectrum GNEM guidance and control method, an original nonlinear optimal control problem is converted into a group of problems for solving a system of linear algebraic equations based on the concept of GNEM through linearization and Gauss pseudo-spectrum dispersion by combining nonlinear approximation model predictive control, linear quadratic optimal control and a Gauss pseudo-spectrum method. The linear pseudo-spectrum GNEM guidance and control method has the advantages that the calculation efficiency of solving the optimal control problem is quite high, and high calculation precision can be obtained just through several nodes; in addition, a final solution can be presented through a smooth function relevant to control over disperse nodes, and the method is quite suitable for online calculation. It is indicated through a simulation result that by applying the method to tail-section attack guidance with terminal angle constraint, compared with an MPSP method, the linear pseudo-spectrum GNEM guidance and control method has higher calculation efficiency and high calculation precision and can be completely applicable to a guidance framework for terminal guidance, and a smaller required overload command is generated compared with self-adaptive tail-section proportion guidance.

The present invention relates to a device and a method for extracting information from detected characteristic signals. A data stream (26) derivable from electromagnetic radiation (14) emitted or reflected by an object (12) is received. The data stream (26) comprises a continuous or discrete time-based characteristic signal ( ; 98) comprising at least two main components (92a, 92b, 92c) related to respective complementary channels (90a, 90b, 90c) of a signal space (88). The characteristic signal ( ; 98) is mapped to a defined component representation ( , , , ; , ) under consideration of a substantially linear algebraic signal composition model so as to specify a linear algebraic equation. The linear algebraic equation is at least partially solved under consideration of an at least approximate estimation of specified signal portions ( , , ). Consequently, an expression highly indicative of the at least one at least partially periodic vital signal (20) can be derived from the linear algebraic equation.

The invention discloses an implicit staggered-grid finite difference elastic wave numerical simulation method and device. The method comprises the steps that a dispersion relation expression is obtained based on an implicit staggered-grid finite difference scheme and a plane wave theoretical formula; (M+1) discrete points are evenly taken within the value range of beta in the dispersion relation expression, and the left and right sides of the dispersion relation expression are set to be equal on the discrete points so that a linear algebraic equation set is obtained; the linear algebraic equation set is solved so that the implicit staggered-grid finite difference coefficient am and constant b are obtained; an elastic wave equation is solved based on the implicit staggered-grid finite difference coefficient am, the constant b and the implicit staggered-grid finite difference format; and a wave field diagram is generated according to the solving result and wave field analysis is performed according to the wave field diagram. The solving error of the elastic wave equation can be reduced and the numerical solution accuracy can be enhanced so that a more accurate wave field stimulation record can be obtained. When the same calculation error is constrained, calculation time can be reduced and calculation efficiency can be enhanced.

The invention provides a power system transient stability digital simulation computation model and an algorithm thereof, and belongs to the field of power system digital simulation. In the traditional machine-network interface algorithm, the conversion computation of a dq axis of each generator is solved in grid node voltage algebraic equations, so that the power system simulation model becomes time variant nonlinear algebraic equations. In the invention, the conversion computation of the dq axis of each generator is solved in a simulation model of each generator set, so that the power system simulation model becomes time invariant linear algebraic equations, and a calculated amount of the power system simulation model during alternate solving is largely reduced. The power system transient stability digital simulation computation employing alternate solving is simplified, a physical significance of the model is clearer, and the programming difficulty is remarkably reduced; and the computation of the simulation model of each generator set during alternate solving is decoupling, so the practical power system transient stability digital simulation parallel computation model can be formed.