The Merits & demerits of different laws to measure a speed-up performances!

Amdahl’s Law

The speed-up factor help us to know the relative gain that is achieved in shifting the execution of a task from sequential computer to parallel computer and the performance does not increase linearly with the increase in number of processor.

Now, Let us consider a problem say P, which has to be solved using a parallel computer. According to Amdahl’s law, there are mainly two types of operations; therefore, the problem will have some sequential operation and some parallel operations. We already know that it requires T (1) amount of time to execute a problem using a sequential machine and sequential algorithm. The time to compute the sequential operation is a fraction ? (?<=1) of the total execution time i.e. T (1) and the time to computer the parallel operations is (1- ?), therefore S (N) can be calculated as under:-

S (N) =T (1)/T (N)

S (N) =T (1)/ (?*T (1) + (1- ?)*T (1)/N)

Dividing by T (1)

S (N) =1/ (?+ (1- ?)/N)

Remember the value of ? is between 0 and 1. Now put some values of number of processors, we find that the S (N) keeps on decreasing with increase in the value of ?.

Speed up Factor S (N) v/s ?

Outcomes of analysis of Amdahl’s Law:-

To optimize the performance of parallel computers modifies compiler need to be developed which aim to reduce the number of sequential operation pertaining to the reaction ?.

Manufacturers of parallel computers were discouraged from manufacturing large scale machine having millions of processors.

One major shortcoming identified in Amdahl’s law: according to Amdahl’s law the problem size is always fixed and of sequential operations remains mainly same.

Gustafson’s Law

There are numerous applications that require that accuracy of the resultant output should be high. In the present situation the computing power has increased substantially due to increase in number of processors attached to parallel computer. Thus it is possible to increase the size of the problem. The graph of speed up:

S (N) =? +N*(1- ?)

S (N) = N- ?*(N-1)

Thus decrease is because of overhead or sizes caused by inter processor communication.

Sun and Ni’s Law

The Sun and Ni’s Law is a generalization of Amdahl’s Law as well as Gustafson’s Law. The fundamental concept of underlying the Sunand Ni’s Law is to find the solution to a problem with a maximum size along with limited requirement of memory. Now a day, there are many applications which are bounded by the memory in contrast to the processing speed.

In a multiple based parallel computer, each processor has an independent small memory. In order to solve a problem, normally the problem is divided into sub problems and distributed to various processors. It may be noted that size of sub-problem should be in proportion with size of the independent local memory available with the processor. The size of the problem can be increased further such that the memory could be utilized. This technique assists in generating more accurate solution as the problem size has been increased.

Arithmetic Pipelining for fixed numbers Multiplication of 8 digit fixed numbers

Following stages for pipelining:

1. The first stage generates the partial product of number, which form the six rows of shifted multiplicands.
2. In second step, the eight are given to the two carry save address merging six numbers.
3. Third step: a single CSA merging the number into 5 numbers.
4. Similarly in next step 5 numbers into 4 number and 4 number into 3.
5. In last step, two numbers are added through a carry propagation adder (CPA) to get the final result. X & Y are two 8 digit fixed number so arithmetic pipeline for multiplication of two 8 digit fixed number is given below:

Perfect shuffle permutation Consider N objects each represented by 4 bits, 4 number say Xn-1, Xn-2, X0. The perfect shuffle of this N object 4 expressed as.

Xn-1, Xn-2, X0 = Xn-2, X0, Xn-1,

This means that perfect shuffle is obtained by rotating the address by 1 bit left.

Shuffle permutation of 32 Nodes:

Close Network:

It is a non-blocking network and provides full connectivity like crossbar network but it requires significantly less number of switches. The organization of close network is shown below using 4 X 4 cross point switches:

This article is a kind of presentation to basics of business communication. In the next up-coming articles, you’ll be able to learn the major pillars and the specifics of business communication.

Communication characteristics and competence

(Significance of communication once approaching a job)

This is the most crucial aspect of the communication that can be considered as one of the major pillars to professionalism. The competency or skill listed most often in job advertisements was communication combined with a variety of adjectives ranging from excellent, the most common to superior, advanced, well-developed, proven, outstanding and natural. Being a team player was most favorite followed closely by interpersonal skills.

An integrated or shared meaning model of communication

Why study communication?

Following four reasons describe the need of the communication.

The growth of technology

Social alienation is growing

Physical well-being

Survival of the human race

Dimensions in communication

Following four objects make the concrete dimension of the business communication.

Verbal

Non-verbal

Mediated

Unmediated

Skill sets

Again there are four observations in communication skill set.

Thinking and feeling

Acting and observing

Speaking and listening

Writing and reading

Levels of communication

There are five major levels of business communication that briefly reveal the sense and existence of the communication.

Level one: intrapersonal communication or the experience of the individual.

Level two: interpersonal communication.

Level three: group communication.

Level four: organizational communication, including:

Internal organizational communication

External organizational communication.

Level five: mass communication

The communication theory

This portion will describe the overall gathered knowledge about communication.

What is a theory?

It explains information or behavior that has been observed.

It is useful because it can be applied to questions about observed behavior to analyze or explain it.

It can be used to suggest solutions to problems, or improvements to a situation.

Why a model?

A model simplifies a theory.

It can aid our thinking about a concept or idea.

It maps something abstract and presents it in a visual form.

It shows the major elements in relationship to each other.

Components of the communication process

Participants

Sender: the participant transmitting the message.

Receiver: the participant receiving the message.

Encoding: the translation of a message (thoughts or ideas of the sender) into words or symbols that the receiver will understand.

Decoding: the translation by the receiver of words or symbols (the encoded message) into thoughts or ideas.

Components of the communication process

Channel: the route through which communication takes place

Context: the situation/environment in which communication occurs. Includes time, place and socio/psychological factors

Perception: a person’s understanding or interpretation of a particular event/message.

Components of the communication process

Purpose: what the sender and receiver intend as the outcome of the communication.

Barriers (sometimes known as noise): anything that interferes with effective communication.

An integrated or shared meaning model of communication

The Principles of communication

We communicate with others: it is a two-way process

Communication is a collection of signals; it is more than words

Communication is always on two levels:

Content & relational

Communication is punctuated

Communication is inevitable

Communication is irreversible

Communication is unrepeatable

Communication is rarely completely understood

Question-1

‘C’

Please solve the equations given below?

You’ll be using the LU decomposition-method

Answer

I got the values as

L11 = 10

L21 = 1

L22 = 101/10

L31 = 2

L32 = 32/10

L33 = 2018/101

U12 = -1/10

U13 = 1/5

U23 = -12/101

Using LUX = B

Let UX = y

LY = B

10y1 = 4

y1 = 4/10

y1 + 101/10 y2 = 3

y2 = 26 /101

2y1 +32/10 y2 + 2018/101 y3 = 7

y3 = 543/2018

Now solving UX = Y

The equation are..

x1 -1/10 x2 + 1/5 x3 = 4/10

x2 – 12/101 x3 = 26/101

x3 = 543/2018 = 0.269

x2 = 58984/203818 = .289

x1 = 76457/203818 = 0.375

You can verify the answer by substituting it in the given equation.

‘D’

Look into the system of equations as given below.

You’ll be using Jacobi iterative-method and will perform three iterations.

This system can be written as

X₁ = 0.5X2 + 0X₃ + 3.5

X₂ = 0.5X1 +0.5X₃ + 0.5

X₃ = 0X1 + 0.5X3 + 0.5

X₁^k+1 = ½ (X₂^k + 7)

X₂^k+1 = ½ (X₃^k + X₁^k + 1)

X₃^k+1 = ½ (X₂^k + 1)

So the Jacobbi iteration is:

No initial iteration is given so we start with X^{0 =} (0, 0, 0)^T

We get the following iteration

X¹ = [3.500 0.500 0.500 ]^T

X² = [3.750 2.500 0.750]^T

X³ = [4.750 2.750 1.750]^T

X⁴ = [4.875 3.750 1.875]^T

After 4 iteration the errors in the solutions are

The solution X⁴ is almost correct to 3 decimal positions.