# Questions tagged [numerical-algorithms]

Questions related to algorithms that use numerical approximations for the problems of mathematical analysis.

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### How to test for overflow when multiplying floats

I am trying to implement a 3-term recurrence relation: $$p_{n+1} = ap_n + bp_{n-1}$$ This can be implemented as ...
145 views

### What is the state of the algorithmic art for floating point arithmetic on complex numbers?

Most modern compilers and processors implement the IEEE 754 binary formats for floating point numbers. IEEE 754 guarantees that the addition, subtraction, multiplication, division, and square root ...
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### Algorithm for using power series to numerically solve a partial differential equation given a boundary condition?

Motivation: Following this discussion about using asymptotic expansions (i.e. polynomial power series) for numerically solving partial differential and algebraic equations (PDAE), I couldn't find any ...
140 views

### Understanding truncation and rounding error in IEEE floating point system?

I'm trying to understand the theory behind finding the optimal $h$ value for differentiation in this definition: $$\frac{f(x+h) - f(x)}{h}$$ as $h$ tends to 0. Here is my understanding: ...
43 views

### Symbolic Math Systems As Speculative Optimization For Numerical Software?

Has there been published work on hiding symbolic math within numeric software, partitioning parallel processes between speculative symbolic optimization search and numeric evaluations? Real world ...
1k views

### Why is adding log probabilities considered “numerically stable”?

Every once in a while, I come across the term numerical stability, which I don't really understand. In particular, I have seen a description of the practice of "adding logs rather than multiplying ...
33 views

### Computation time of a Binom matlab (or C) routine

I am trying to write a Matlab (or C) routine for the exact probability F of observing K or more successes when a success probability P is expected ($\sum_{k=i}^n \binom{n}{k}p^k(1-p)^{n-k}$). I am ...
66 views

### Union of fixed and floating point types

Say I have two real number types. They may be floating or fixed point. How can I construct a new type whose values are at least the union of the two with the minimal number of bits? There are 3 cases ...
923 views

### How approximate sine using Taylor series

I need to approximate the sine function without internal libraries. I used Taylor series in 0 to solve this, but my program works for some values, but for others awful results. The program gets x ...
58 views

### Naviers Stokes equation and machine learning

I am looking for a reference explaining how to solve Navier-Stokes numerically using Machine learning algorithms . Thank you in advance for your help .
72 views

### Efficiently compute parallel matrix-vector product for block vectors with FFTs?

Assume I have $P$ processors, each having a different vector $v_p$ of size $N$, $p=1, ..., P$. I learned in this question/answer that for computing the matrix-vector product $$w = (E\otimes I_N)v$$ ...
50 views

### Efficiently compute parallel matrix-vector product for block vectors?

I have $P$ processors, each having a different vector $v_p$ of size $N$, $p=1, ..., P$. I now want to compute the matrix-vector product $$w = (E\otimes I_N)v$$ in parallel, where $\otimes$ is the ...
141 views

### UInt128 - Compute the product of two UInt128's that are each represented by two UInt64's?

I have a struct like this: struct UInt128 { UInt64 s1; UInt64 s2; } In this struct, s1 represents the highest 64-bits ...
132 views

### What is the role of Numerical Gradient Computation in Backpropagation algorithm?

I was listening CS231n (2017) lectures and noted that there is a lot of attention to Numerical Gradient Computation (NGC). It starts @5:53 in this video and appears a few times later. Also, looking ...
132 views

### Algorithm to find extrema of a function?

What are some simple algorithms that find the maximum of a function in a certain domain? The function $f$ is guaranteed to have 1 maximum and no other turning points between $a$ and $b$, how can I ...
Suppose we are given a matrix $A$ over real numbers and we want to computer the inverse of matrix $A$. There are various algorithms to do so and it also turn out that we can use matrix multiplication ...