48 results about "Solution of equations" patented technology

The present invention relates to a solution-finding method, which finds an approximate solution of an equation having difficulty in obtaining an actual solution and a complicated equation in numerical analysis. The method obtains an approximate solution of an equation having a solution in a predetermined interval. Initial values are calculated based on upper and lower limits of the interval. The initial values are applied to a solution-finding equation, including a sign function and the upper and lower limits, and the solution-finding equation is arranged so that a definite integral formula for the sign function is included in the equation. The definite integral formula in the solution-finding equation is calculated using numerical integration, and results of the definite integral formula are applied to the solution-finding equation, thus obtaining an approximate solution. This performance is iterated until the approximate solution satisfies an allowable error.

The invention provides a surface intersection method, which comprises the following steps of: dividing surfaces into small crossed areas; determining a starting point; constructing a surface intersection equation in two unknowns; solving the surface intersection equation in two unknowns; and constructing lines of intersection according to roots of the equation in two unknowns. Therefore, the method effectively improves the iteration efficiency, the tracking step length and direction determination precision and the accuracy at the nearly overlapping of the surfaces in the process of performing the surface intersection by utilizing a tracking method.

A system for evaluating the convergence to a solution for a matrix equation comprises at least one reconfigurable computing device such as a field programmable gate array (FPGA), an update storage element, a conversion element, a summation unit, and a comparator. The FPGA includes a plurality of configurable logic elements and a plurality of configurable storage elements, which are utilized to form the update storage element, the conversion element, the summation unit, and the comparator. The update storage element is configured to store a plurality of updates. The conversion element determines the absolute value of the updates. The summation unit accumulates the absolute values of the updates to produce a total sum, which is compared to a convergence factor by the comparator. Convergence is signaled when the total sum is less than the convergence factor.

The invention discloses a calibration device and a method for carrying out calibration on a transfer function in a monitoring device. The method comprises the steps: setting m parameters of the transfer function as parameter values of first iteration; carrying out at least one iterative process; in a jth iterative process, if a calculated error evaluation value s is smaller than an evaluation target value according to AD1-ADn, Rxp1-Rxpn, and a parameter value of jth iteration, confirming the parameter value of the jth iteration as a calibration result; if not, adjusting the parameter value of the jth iteration according to a shrinkage algorithm, obtaining a parameter value of j+1th iteration, and continuing the next iterative process, wherein the Rxp1-Rxpn are n index values of a monitored object, and the AD1-ADn are n sampling values. Due to the fact that the shrinkage algorithm is adopted to carry out iterative calculation on the parameters of the transfer function, the process of missing solution of equations is avoided, the method can be applied to situations of a non-linear transfer function and a non-least-square error evaluation function, and accordingly the calibration method has wide application situations.