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1. Nurul Nabila Nadzira

2. Ruz Hadzirah Ezreen

3. Fara Nabilah

4. Muhammad Izzat

5. Nurin Adani

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Nur Annisa Binti Anday Shaibullah

A21EB0056

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In Newton Interpolation,the interpolating polynomial is expressed as a sum of terms, rovides a sequence of polynomials, each one adding a new data point, forming a polynomial of increasing degree and uses the concept of divided differences to calculate the coefficients of the interpolating polynomial.

In Lagrange Interpolation,the interpolating polynomial is expressed as a linear, yields a single polynomial that passes through all the data points. It is a direct method for constructing the interpolating polynomial, does not involve divided differences explicitly.

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Wang Jiayi

A20EB4012

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Quiz individu: Ahmad Shahrul bin Abdul Wahid

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Najwa Afiffah binti Mohd Fauzi

A20EB3002

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Nur Aqilah Syasya binti Mohamad Najib

A20EB3003

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Quiz Individual - Maria Alessandra Sabiniano Florida (A20EB4009)

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Quiz Individual - Maria Alessandra Sabiniano Florida (A20EB4009)

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AHMED AB ALAREF

A20EE4003

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Muhammad Arieff Danial Bin Roslan

A21EE0130

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Nivea Nur Masud

A19EE4022

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Siti Nurbalqis binti Jaanavaskhan

A22EE0307

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Alex Gabriel Anak Millton (A21EE0012)

Lagrange's form is more efficient when we have to interpolate several data sets on the same data points.

Newton's form is more efficient when we have to interpolate data incrementally.

The advantage of Newton interpolation is the use of nested multiplication and the relative easiness to add more data points for higher-order interpolating polynomials.

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Qhairun Sofea Binti Mohd Zairadi
A21EB0073

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Nur Hidayahtul Fitrieah Binti Roslan

A21EB0060

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Muhammad Aliff Haiqal bin Mohd zamri(individual quiz)

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Muhammad Aliff Haiqal bin Mohd zamri(individual quiz)

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The most flexible interpolation technique is Lagrange's formula, which is simple to understand, does not require evenly spaced interpolation points, and can also be used for inverse interpolation. Its flaw is that it requires too many calculations, which increases the likelihood of errors when doing calculations by hand.Although Newton's Divided Difference interpolation is quicker to calculate and does not require equal spacing as Lagrange's, its reasoning is less clear-cut and does not directly support inverse interpolation.

2. In the case of evenly spaced points, Newton-Gregory forward and backward interpolation is the quickest application of the Divided difference formula.

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Muhammad Faizzudin Bin Leezam

A21EE0136

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section 9

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Lagrange interpolation is mostly just useful for theory. Actually computing with it requires huge numbers and catastrophic cancellations.

In floating point arithmetic this is very bad. It does have some small advantages: for instance, the Lagrange approach amounts to diagonalizing the problem of finding the coefficients, so it takes only linear time to find the coefficients. This is good if you need to use the same set of points repeatedly.

For Newton interpolation, you get the coefficients reasonably fast (quadratic time), the evaluation is much more stable (roughly because there is usually a single dominant term for a given x).

It is also fairly easy to see how to interpolate derivatives using the Newton framework.

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NURHUMAIRA' AISYAH BINTI MAHATHAR A21EB0067

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WAN HAZIQ SHAKIRIN BIN WAN HASNAN

A21EE0214

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NUR AIYANI BT MUHAMMAD FAUZI

A21EB0054

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Zairyl Daniel Bin Zulhamidi (A21EE0227)

Newton Interpolation uses the divided difference formula to construct the interpolation polynomial, while Lagrange Interpolation uses Lagrange polynomials. In Newton Interpolation, the polynomial is represented as a sum of terms with divided differences and basis polynomials. It's efficient for adding new data points.

Lagrange Interpolation, on the other hand, uses a set of basis polynomials associated with each data point. The polynomial is the sum of these basis polynomials, multiplied by the data point values. It's straightforward but computationally expensive for adding new data points. The choice depends on factors like dataset size and specific requirements.

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Muhammad Faiz Bin Rozuki

(A20EE0144)

From my understanding, Lagrange Interpolation

Use the sum of basis polynomial which related with the set of data, and this sum is related to the number of set data, which could require quite a lot of computational cost if its dealing with a large number of set data.

As for Newtons Interpolation,

Is use to find missing data in a set of data, there are three ways to use Newtons Interpolation depending which set of data are we want.

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Mohammed Saif Ahmed Alwaqedi

Lagrange interpolation employs Lagrange polynomials, whereas Newton interpolation uses the divided difference formula to get the interpolation polynomial. The polynomial is expressed in Newton Interpolation as the sum of terms with split differences and base polynomials. It works well for adding new information.

Conversely, Lagrange Interpolation makes use of a collection of basis polynomials that are connected to every data point. The polynomial is obtained by multiplying the values of the data points by the sum of these basic polynomials. Simple in theory, but computationally costly when adding additional data points. The decision is based on variables such as the size of the dataset and particular needs.

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Albarraa Hussein Osman

Isra Altyeb

Hibat Alwaleed

Nivea Nur Masoud

Ahmed Ab Alaref

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Syahzanani Zawanah binti Abdul Taip (A21EE0201)

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Syahzanani Zawanah binti Abdul Taip (A21EE0201)

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Muhammad Hifzanuddin bin Mohd Shahiman (A21EE0271)

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Muhammad Hifzanuddin bin Mohd Shahiman (A21EE0271)

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MOHAMAD DANIEL HAZIQ BIN HASWADI (A21EE0103)

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MOHAMAD DANIEL HAZIQ BIN HASWADI (A21EE0103)

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Muhammad Imran bin Abu Bakar

A21EE0150

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Newton's interpolation method and Lagrange interpolation are two popular techniques for approximating a polynomial that passes through a given set of data points. In Newton's method, the interpolation polynomial is expressed using divided difference polynomials as basis functions. These basis polynomials involve incremental differences between data points and are calculated recursively. The interpolation polynomial is then represented in terms of these divided differences, providing a convenient form for computation. On the other hand, Lagrange interpolation employs Lagrange basis polynomials as its basis functions. The Lagrange interpolation polynomial is expressed as a sum of terms, each term being a Lagrange basis polynomial multiplied by the corresponding function value at the associated data point. Unlike Newton's method, Lagrange interpolation directly constructs the polynomial without the need for recursive calculations. While both methods serve the same purpose of polynomial interpolation, the choice between them often depends on the specific requirements and preferences of the problem at hand.

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Muhammad Nasrul Nasruddin bin Narudin (A21EE0158)

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Chan Kah Chun A21EE0233

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A22EE0280

Individual quiz

Newton's Interpolation Method:

Uses divided difference coefficients to construct the interpolating polynomial.

Requires the computation of finite differences between data points.

Suitable for incremental addition of data points without recalculating the entire polynomial.

Lagrange Interpolation:

Constructs the interpolating polynomial directly using Lagrange basis polynomials.

Doesn't require calculating differences between data points.

Simpler in terms of computation but may become less efficient for large datasets.

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A21EE0004

Newton's Interpolation Method: Builds the interpolating polynomial using divided difference coefficients. demands that the finite differences between data points be calculated. appropriate for adding data points one at a time without having to recalculate the polynomial in its entirety.

Lagrange Interpolation: This method uses Lagrange basis polynomials to directly construct the interpolating polynomial. does not necessitate computing the disparities between data points. simpler to calculate, however it might become less effective with bigger datasets.

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IRSYAD NAZHAN BIN ROSLI(INDIVIDUAL QUIZ)

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IRSYAD NAZHAN BIN ROSLI(INDIVIDUAL QUIZ)

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Lagrange's form is preferable for interpolating multiple data sets at common data points

Newton's form is better suited for incremental data interpolation.

Newton's interpolation involves nested multiplication, making it convenient to incorporate additional data points for constructing higher-order interpolating polynomials.