Genreg: A fortran programme for multivariate interpolation by generalized regula falsi

The secant or regula falsi method for solving the equation f(x)=0 for one variable X is well known. This has been generalized to n variables by L. Fox and R. sankar(1) for the determination of zeros of a function of n variables. the geneeralized algorithm can also be used to perform multivariate interpolation is presented in this report

Lapeqs: A Fortran programme to solve laplaces equation

The curves PQ and RS lie in the closed interval (a,b) and. they are given as a set of ordinates.The problem is to solve in the region PQRS. The subroutine contructs a grid in the region PQRS, numbers the grid points alonG the grid lines and sets up the Laplace difference equation at each grid point using 3-point finite difference fcrmulae for the derivatives.The set of these difference equations is banded and is solved by Liebmann's iterative technique. Successive over-relaxation is employed to speed up the convergence of the iteration if invoked the user and if he provides the SOR factor. The subroutine provijes good starting approximations for the potentials at each grid point by assuming linear variation along each vertical grid lineo In most cases this is found to result in fast convergence and consequently considerable saving of computer time

Solution of a large set of simultaneous linear equations by matrix partitioning using random access storage

The solution of a set of linear algebraic equations has always been a fascinating and challenging field, justifying a lot of research investigation. The advent of digital computers has greatly facilitated these investigations and made it possible to extend the solution procedure to larger systems. However9 the physically available core memory of the computer can restrict the problem size. This difficulty can be overcome by using random access devices such as magnetic drums and discs. In this report we present an algorithm which can be adapted to a system having random access storage

Curve fitting with end-constraints based on a modification of Hiroshi-Akima's method

The method of Hiroshi Akima gives a curve which ensures - smoothness of first derivatives at the data points. The method consists of fitting cubic polynomials between every Pair of Doints (x1,y1.), 1 = l(l)n. The slope of the tangent tk to the curve at a specific point (xk' Yk) is obtained lecally by using the; coordinates of the five points (xk-2' Yk-2)' (Xk-l' Yk-l)'13; quot; (Xk' Yk)' (xk+l' Yk+l) and (Xk+2' Yk+2) of which (xk'Yk)13; is the middle member, Let the slopes of secant joining13; quot; (Xk' Yk) and (xk+l' Yk+l) be mk

Ancient crustal metamorphism at low pH2O: Charnockite formation at Kabbaldurga, South India

Arrested charnockitic conversion of amphibolitic gneiss at Kabbaldurga, Karnataka State, south India, was studied mineralogically. Iron-rich pyroxenes were generated from amphibole in patches and stringers without melting. The dark colour of charnockite arises from numerous tiny veins of chlorite and manganese-bearing calcite, particularly in feldspars. The metamorphism was effected by very local, mainly grain-boundary, migration of volatiles low in H2O, and probably dominantly CO2. This was followed by vein alteration at lower temperatures from volatiles richer in H2O. The volatiles are ascribed to massive liberation from the mantle in upwelling areas, and this may have been an important process in the evolution of the deep continental crust. © 1979 Nature Publishing Group