All Questions
Tagged with floating-point linear-algebra
10
questions
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66
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Proof of loss of orthogonality in Gram-Schmidt
I am stuck at understanding about how to derive the following proofs related to error bounds which are given in the following slides. Can anyone please explain to me how these are derived?
1
vote
1
answer
461
views
Rounding error of matrix multiplication when one of the matrices is orthogonal
I am studying Scientific computing from Biswa Nath Datta's Numerical Linear Algebra and Applications and there is a corollary after explaining matrix multiplication rounding error described below.
if $...
0
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0
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349
views
Unique single value for a 3D point
I have 3D points like this:
Vertex {
X float
, Y float
, Z float
}
Is there any single value of type float or ...
- 271
1
vote
1
answer
274
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LU-factorization and floating-point operations
The LU-factorisation of $A\in\mathbb{R}^{n\times n}$ is given by $$A=LU,$$ where $L$ is a unit lower triangular matrix and $U$ is an upper triangular matrix.
I am trying to understand why it ...
- 617
9
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2
answers
1k
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Conditioning of the linear systems in the inverse or Rayleigh quotient iteration algorithms
I'm working through the book Numerical Linear Algebra by Trefethen and Bau. In Lecture 27 (and exercise 27.5), the following claim is made about the inverse iteration algorithm:
Let $ A $ be a real, ...
- 323
1
vote
1
answer
5k
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Working out operation counts for matrix-vector multiplication
I'm working on a problem about the multiplication of a matrix $A$ of order $m \times n$ by a vector $b$. In particular I'm supposed to determine the number of operations needed.
What is the point of ...
- 11
1
vote
0
answers
80
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How do we tell arithemetic addition or subtraction from floating point numbers?
Source: C++ for Engineers and Scientists, Gary J. Bronson
Source: Programmable Logic Controllers: The Complete Guide to the Technology by Clarence T. Jones
In the table $12345.67_{10}$ = 1.234567+04 (...
- 1,530
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votes
1
answer
251
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How do I perform Gram-Schmidt on floating point vectors with epsilons in them?
Let $\epsilon$ be a small positive number such that $1+\epsilon$ and $3+2\epsilon$ are machine numbers but $3+2\epsilon + \epsilon^{2}$ is computed to be $3 + 2\epsilon $. Now, let the (classical) ...
user100463
0
votes
1
answer
717
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Floating Point Number System
I really have no idea of how to do these questions - in fact I have no idea of how to do any question in the paper - but I have tried to figure out what's going on in the course called Computational ...
- 471
3
votes
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363
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Check for Ill Conditioned matrix
How can I efficiently check if a tridiagonal system with 1's in diagonal is ill-conditioned or not ? The common way is to get the ratio of largest and smallest singular values and see if its greater ...
- 109