Yossi Peretz

11 Questions 6 Answers 0 Followers

Questions related from Yossi Peretz

I need a reference to a proof of inapproximability of Linear Equations Over The Nonegative Integers Restricted To Some Region. Can anyone help?

Let A be an nxn matrix of integers and b be an nx1 vector of integers. Then, the problem: "Does there exist a vector of nonnegative integers x such that Ax=b?" is known to be NP-Complete. Assume...

11 February 2023 1,407 0 View

I need a refernce for the proof that C and C(x) are isomorphic. Can anyone give such reference?

Let C denote the field of complex numbers and let C(x) denote the field of rational functions over C, with variable x. I know that C and C(x) are isomorphic. Can one give a reference for the...

03 February 2022 8,241 0 View

Let V denote a vector space over the field of rational functions. Is there any way to define an inner product on V?

Let C(z) denote the field of rational functions (over the complex field), where z=(z_{1},...,z_{k}). Let V=C(z)^{n}. Is there any way to define an inner product on V? If affirmative, could you...

24 January 2022 2,061 0 View

Regarding unique solution for Sylvester equation over finite field, is there any equivalent condition in terms of minimal polynomials of the matrices?

Let A,B nxn matrices over finite field F. One can prove that if the minimal polynomials of A,B are co-prime then the Sylvester equation AX-AB=C has uniqe solution for any given matrix C over F. Is...

13 May 2019 8,078 6 View

What is the condition for unique solution for the Sylvester equation over the field F_{2} ?

I'm looking for a necessary and sufficient condition for unique solutions to the Sylvester matrix equation AX-XD=B over the field F_{2}. Does anybody know about such condition that involves the...

25 February 2019 594 1 View

Does the FFD approximation algorithm for the Bin Packing Problem proves P=NP !?

I have the following two facts about the Bin Packing Problem that seemingly proves that P=NP ! Let FFD denote the First Fit Decreasing approximation algorithm for the BP problem. Then, we have...

23 January 2019 5,717 3 View

What is the best known parallel algorithm for matrix inversion over finite field ?

In the article "Fast Parallel Computation of Characteristic Polynomial by Leverrier's Power Sum Method Adapted to Fields of Finite Characteristic" by Arnold Schonhage 1993, the author represets an...

13 January 2019 8,307 1 View

What is the best algorithmic method to solve multivariable quadratic polynomial system of equations over finite fields ? What is its complexity ?

Given an overdetermined set of quadratic multivariable polynomial equations over some finite field F_{q}, what is the best known algorithm to solve the problem and what is its complexity ? What...

08 January 2018 1,828 1 View

What is the probability that the nonsymmetric algebraic Riccati equation XCX-XD+AX-B=0 has solutions ?

Let T=[A B;C D] be a real (m+n)X(m+n) stable matrix with controllable pair (D,C). Choosing such matrices T uniformly at random: What is the probability that the nonsymmetric algebraic Riccati...

21 December 2015 7,257 3 View

What is the complexity of regional pole placement in non-convex or unconnected regions ?

It is known that exact pole placement is NP-hard. On the other hand it is known that regional pole placement in LMI regions can be solved in polynomial time. The question is what is the complexity...

16 April 2015 5,224 3 View

Does anyone have experienced with HIFOO ?

How can I use HIFOO in order to find a minimal-norm static-output-feedback ? Specifically, if A,B,C are the state space matrices of a continuous time linear system, how can I find, using HIFOO, a...

28 October 2014 5,578 2 View