A new Numerical Method (US patent application no. 15/797649; US application publication no. US 2018-004151 A1) first of its kind in about 200-years is propounded by the following 5-statements:
A. Organize linear or nonlinear equations as mismatch functions equated to zero.
B. In each of the mismatch functions, club any term with known quantities or value into a diagonal term with simple algebraic manipulations.
C. Express a vector of the mismatch functions as a product of a coefficient matrix and a vector of unknown variables, which can sometimes be treated as a correction vector of unknown variables.
D. Equate the vector of mismatch functions to the product of the coefficient matrix and the vector of unknown variables or the correction vector of unknown variables to be calculated.
E. Solve such a matrix equation by iterations for the vector of unknown variables or the correction vector of unknown variables using evaluation of the vector of mismatch functions with guess values of unknown variables to begin with, and inverting or factoring the coefficient matrix.
All possible applications of the new numerical method in different subject areas can be developed including steady state power network analysis referred to as loadflow computation. A new class of Loadflow Computation Methods (LCMs) are invented that can be more efficient and reliable in providing converged solutions compared to all known Newton-Raphson (NR) numerical method based LCMs.
Each of the developed applications of the new numerical method (or can also be each of the NR based applications) in different subject areas can be used for generating (not storing – eliminating the need for data storage) input-output training and validating data sets (as per US patent no. 8756047) for training, validating, and storing corresponding Artificial Neural Network (ANN) that can act as solution (calculation) robot in the sense that give required inputs and get relevant outputs(solution) using corresponding Trained, Validated, and Stored ANN.
There could be a single ANN like a single black-box with N-number of inputs and N-number of outputs for the solution of N-number of simultaneous algebraic equations. However, it is proposed to have a separate ANN for each output, and each ANN requires the same N-number of inputs. That means there are as many ANNs as number of outputs, and all of them can be trained and validated in parallel on a separate processor making training and validating process fast that can further be enhanced by restricting number of inputs to each ANN by a feature selection technique. The feature selection technique involves selecting the inputs that affect an output the most, and one such technique is presented in the US patent no. 8756047.
A new business model that emerges is Software as Service as well as High Performance Computing as Service based on all possible applications of the new numerical method wherein all application software and corresponding trained ANNs reside in a data center and online services can be provided. Revenue model could be advertisement based or subscription based or any combination.