A function fitting method
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Rajesh Dachiraju
Abstract
In this article, we describe a function fitting method that has potential applications in machine learning and also prove relevant theorems. The described function fitting method is a convex minimization problem which can be solved using a gradient descent algorithm. We also provide qualitative analysis on fitness to data of this function fitting method. The function fitting problem is also shown to be a solution of a linear, weak partial differential equation (PDE). We describe a simple numerical solution using a gradient descent algorithm that converges uniformly to the actual solution. As the functional of the minimization problem is a quadratic form, there also exists a numerical method using linear algebra.
Dedicated to the memory of my father D. Narasimharaju (1951–2010), a mathematics teacher who inspired me
Acknowledgements
The author is thankful to the math-stackexchange and mathoverflow communities.
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Articles in the same Issue
- Frontmatter
- On the steady-states of a two-species non-local cross-diffusion model
- Iterative techniques with computer realization for initial value problems for Riemann–Liouville fractional differential equations
-
Existence of positive solutions of a new class of nonlocal
- A function fitting method
-
Some Hermite–Hadamard type integral inequalities for convex functions defined on convex bodies in
- Some properties of modified Szász–Mirakyan operators in polynomial spaces via the power summability method
- Some sufficient conditions for univalence and close-to-convexity
- Approximation by Stancu–Chlodowsky type λ-Bernstein operators
- Radius problems for univalent functions
- Convergence theorem for a finite family of asymptotically demicontractive multi-valued mappings in CAT(0) spaces
- Transforming linear time-varying optimal control problems with quadratic criteria into quadratic programming ones via wavelets
- Delaunay surfaces expressed in terms of a Cartan moving frame
