Method and apparatus for approximating a function
Embodiments described herein provide techniques for computing an approximation of a function. These embodiments provide an iterative method that avoids the computation of the normal matrix and/or the coefficients, as is typical in the prior art. (See diagram 600, for example.) The iterative method works on the functions directly. At each iteration, the approximating function is computed directly. (See diagram 200. ) Since there is no need to compute the normal matrix or the coefficients of the basis functions, this approach avoids the overhead associated with them, and therefore, increases the speed of computation and reduces resource requirements. For example, various embodiments are suitable for implementation on hardware devices such as on an FPGA or an ASIC.
1 . A method for approximating a function comprising:
utilizing a stochastic conjugate gradient method (SCG) to iteratively compute a first approximating function using a set of basis functions;
using the first approximating function in the generation of output data;
compute a second approximating function using the output data.
2 . The method as recited in claim 1 , wherein utilizing an SCG to iteratively compute the first approximating function comprises
utilizing an SCG for multivariate functions to iteratively compute the first approximating function.
3 . The method as recited in claim 1 , wherein utilizing an SCG to iteratively compute the first approximating function comprises
utilizing a stochastic conjugate gradient method on functions (SCGF) to iteratively compute the first approximating function
4 . The method as recited in claim 3 , wherein utilizing an SCGF to iteratively compute the first approximating function comprises
utilizing an SCGF for multivariate functions to iteratively compute the first approximating function.
5 . A method for approximating a function comprising:
utilizing a stochastic conjugate gradient method (SCG) to compute a first approximating function using a set of basis functions and a first set of input data and a first set of output data;
generating a second set of output data using the first approximating function;
computing a second approximating function using a second set of input data and the second set of output data.
6 . The method as recited in claim 5 , wherein utilizing an SCG to compute the first approximating function comprises
utilizing an SCG for multivariate functions to compute the first approximating function.
7 . The method as recited in claim 5 , wherein utilizing an SCG to compute the first approximating function comprises
utilizing an SCG in which functions are represented by look-up-tables to compute the first approximating function.
8 . The method as recited in claim 5 , wherein utilizing an SCG to compute the first approximating function comprises
utilizing a stochastic conjugate gradient method on functions (SCGF) to compute the first approximating function
9 . The method as recited in claim 8 , wherein utilizing an SCGF to compute the first approximating function comprises
utilizing an SCGF for multivariate functions to compute the first approximating function.
10 . The method as recited in claim 5 , wherein utilizing an SCG to compute the first approximating function comprises
utilizing an SCG with multiple iterations to compute the first approximating function.
11 . The method as recited in claim 5 , further comprising
computing a residual using the first set of input data and the first set of output data;
computing a search direction based on the residual and the set of basis functions.
12 . The method as recited in claim 11 , wherein computing the second approximating function using the second set of input data and the second set of output data comprises
computing the second approximating function additionally using the search direction.
13 . The method as recited in claim 5 , wherein generating a second set of output data using the first approximating function comprises
using the first approximating function as a predistorter.
14 . A function approximator comprising:
interface circuitry; and
logic circuitry, coupled to the interface circuitry,
adapted to utilize a stochastic conjugate gradient method (SCG) to iteratively compute a first approximating function using a set of basis functions,
adapted to receive via the interface circuitry output data generated using the first approximating function, and
adapted to compute a second approximating function using the output data.
15 . The function approximator as recited in claim 14 , wherein the logic circuitry comprises at least a portion of a field-programmable gate array (FPGA).
16 . The function approximator as recited in claim 14 , wherein the logic circuitry comprises at least a portion of an application-specific integrated circuit (ASIC).
17 . The function approximator as recited in claim 14 , wherein the logic circuitry comprises a memory unit.