## View abstract

### Session S34 - Symbolic and Numerical Computation with Polynomials

Friday, July 16, 15:15 ~ 15:45 UTC-3

## Towards correct and efficient computations with polynomials

### Michael Burr

#### Clemson University, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak95d3a07a57f215b028c41a702bbdc7e2').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy95d3a07a57f215b028c41a702bbdc7e2 = 'b&#117;rr2' + '&#64;'; addy95d3a07a57f215b028c41a702bbdc7e2 = addy95d3a07a57f215b028c41a702bbdc7e2 + 'cl&#101;ms&#111;n' + '&#46;' + '&#101;d&#117;'; var addy_text95d3a07a57f215b028c41a702bbdc7e2 = 'b&#117;rr2' + '&#64;' + 'cl&#101;ms&#111;n' + '&#46;' + '&#101;d&#117;';document.getElementById('cloak95d3a07a57f215b028c41a702bbdc7e2').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy95d3a07a57f215b028c41a702bbdc7e2 + '\'>'+addy_text95d3a07a57f215b028c41a702bbdc7e2+'<\/a>';

Traditionally, there has been a trade-off between efficiency and correctness when deciding between symbolic and numeric computations. Hybrid symbolic-numeric computations can avoid this trade-off and be both efficient and correct. Such hybrid methods have been particularly fruitful in algorithms for solving polynomial systems.

In this talk we will discuss a new framework for the design of hybrid symbolic-numeric computations. This framework is devised to expose the key details so that both the efficiency and the correctness of the developed algorithms can be studied directly. We will illustrate this framework on algorithms for finding the isolated roots of systems of polynomials.

Joint work with Chee Yap (New York University) and Juan Xu (Beihang University).