QR decomposition is widely used for solving the least squares problem. However, existing materials about it may be too abstract for non-mathematicians, especially STEM students, and/or require serious background in linear algebra. The paper describes theoretical background and examples of GNU Octave compatible MATLAB scripts that give relatively…

Useful programming tricks are suggested to allow the reduction of many equations and non-polynomial-like expressions and the subsequent application of the mathematical algorithms. (Author)

In this paper a reliable method is found for approximating the value of the Bivariate Normal Correlation Coefficient, rho, given values of the joint probability and the normal deviates, h and k, or the related areas. This technique finds useful application in the computation of the tetrachoric correlation coefficient, r, when the underlying…

Relations between maximum likelihood factor analysis and factor indeterminacy are discussed. (CK)

The calculator is used to solve certain formidable equations, which arise naturally and which may be difficult or impossible to solve by standard methods, by a method of successive approximations. (MP)

Presents new least-squares algorithms that update a fit after each point is entered so trends can be detected promptly as an experiment proceeds. (MLH)

Examines problem-solving results among second-grade students in three schools that were all using a reformed mathematics curriculum. Except for one problem, more students used a mental procedure than the standard written algorithms, and both methods were used with approximately the same degree of accuracy. (AIM)

Four different types of problems from graph theory are presented and discussed. (MK)

Discusses a numerical technique called the method of adjoints, turning a linear two-point boundary value problem into an initial value problem. Described are steps for using the method in linear or nonlinear systems. Applies the technique to solve a simple pendulum problem. Lists 15 references. (YP)

A new heuristic factorization scheme uses learning to improve the efficiency of determining the symbolic factorization of multivariable polynomials with interger coefficients and an arbitrary number of variables and terms. The factorization scheme makes extensive use of artificial intelligence techniques (e.g., model-building, learning, and…

Presented are the results of a study conducted to develop algorithms for ordering and organizing data that can be presented in a two-dimensional matrix form. The purpose of the work was to develop methods to extract latent data patterns, grouping, and structural relationships which are not apparent from the raw matrix data. The algorithms…

The patterns of the coefficients in the expansion of (x + y +z)n are discussed, and a recursive property is developed as a generalization of the Pascal triangle. (MP)

Reviews the mathematical properties of algorithms and problems which can not be resolved by present methods in mathematics. (SL)

Possible ways of mechanization for counting using a binary system are discussed. Shows a binary representation of the numbers and geometric models having eight triples of lamps. Provides three problem sets. (YP)