FEB 7, 2020 | 11:45 AM TO 12:45 PM
Details
| WHERE: | The Graduate Center 365 Fifth Avenue |
| ROOM: | 4419 |
| WHEN: | Feb 7, 2020: 11:45 AM-12:45 PM |
| ADMISSION: | Free |
Description
Abstract: Algorithms of numerical analysis assume by default that all numbers manipulated by the computer are real numbers. We introduce for the first time in this talk a numerical method that accommodates the internal coarse binary operations of a computer to increase the efficiency of the algorithm. We show that a linear system of equations with a matrix that is symmetric and positive semidefinite can be iteratively solved with an algorithm where every multiplication is reduced to a scaling by a power of 2, which simply amounts to bit shifts in binary.
We will then see how this multiplierless algorithm can be used in various problems, such as least squares, l1-regularized least squares and the minimal-norm resolution of any consistent linear system. A particular application of focus will be the minimal-norm reconstruction of a bandlimited signal from generalized nonuniform samples.
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