Weeks 3 and 4
Week 3
I started work on using the automatic slope evaluation algorithm to improve efficiency of the one-dimensional interval Newton method PR #73. Following this, I extended one-dimensional slope evaluation algorithm, which was analogous to the derivative of a function to the multidimensional case, which can be thought of as analogous to the Jacobian. There were some challenges in accomplishing this, but resorting to some good, old calculus and scribbling on loose sheets worked out well. PR #76.
Week 4
In the fourth week, I started working on one of the major parts of my proposal, root finder for a system of non-linear equations. It works by approximating the system as a linear equation and then iteratively solving for the root. The smaller the interval, the better the approximation. So, for a more efficient algorithm, a better linear equation solver was needed. That’s why I implemented the linear hull method PR #79, which gives a tighter bound on the solution set and requires fewer iterations to converge for the multidim Interval Newton Method which was the major work done during this week. PR #81
Moving Forward
I am on track according to my GSoC timeline, and plan to continue the same. Also, I have been thinking of parallelly implementing the future weeks’ work such as Global Optimisation and the like.
Also, I booked tickets for JuliaCon ‘18 and am really excited to be there. Thanks a lot to Julia and NumFOCUS for the oppurtunity! Cheers!